The narrative of Fun Home is non-linear and recursive. Incidents are told and re-told in the light of new information or themes. Bechdel describes the structure of Fun Home as a labyrinth, "going over the same material, but starting from the outside and spiraling in to the center of the story." In an essay on memoirs and truth in the academic journal PMLA, Nancy K. Miller explains that as Bechdel revisits scenes and themes "she re-creates memories in which the force of attachment generates the structure of the memoir itself." Additionally, the memoir derives its structure from allusions to various works of literature, Greek myth and visual arts; the events of Bechdel's family life during her childhood and adolescence are presented through this allusive lens. Miller notes that the narratives of the referenced literary texts "provide clues, both true and false, to the mysteries of family relations."
The memoir focuses on Bechdel's family, and is centered on her relationship with her father, Bruce. Bruce Bechdel was a funeral director and high school English teacher in Beech Creek, where Alison and her siblings grew up. The book's title comes from the family nickname for the funeral home, the family business in which Bruce Bechdel grew up and later worked; the phrase also refers ironically to Bruce Bechdel's tyrannical domestic rule. Bruce Bechdel's two occupations are reflected in Fun Home's focus on death and literature.
In the beginning of the book, the memoir exhibits Bruce Bechdel's obsession with restoring the family's Victorian home. His obsessive need to restore the house is connected to his emotional distance from his family, which he expressed in coldness and occasional bouts of abusive rage. This emotional distance, in turn, is connected with his being a closeted homosexual. Bruce Bechdel had homosexual relationships in the military and with his high school students; some of those students were also family friends and babysitters. At the age of 44, two weeks after his wife requested a divorce, he stepped into the path of an oncoming Sunbeam Bread truck and was killed. Although the evidence is equivocal, Alison Bechdel concludes that her father committed suicide.
The story also deals with Alison Bechdel's own struggle with her sexual identity, reaching a catharsis in the realization that she is a lesbian and her coming out to her parents. The memoir frankly examines her sexual development, including transcripts from her childhood diary, anecdotes about masturbation, and tales of her first sexual experiences with her girlfriend, Joan. In addition to their common homosexuality, Alison and Bruce Bechdel share obsessive-compulsive tendencies and artistic leanings, albeit with opposing aesthetic senses: "I was Spartan to my father's Athenian. Modern to his Victorian. Butch to his nelly. Utilitarian to his aesthete." This opposition was a source of tension in their relationship, as both tried to express their dissatisfaction with their given gender roles: "Not only were we inverts, we were inversions of each other. While I was trying to compensate for something unmanly in him, he was attempting to express something feminine through me. It was a war of cross-purposes, and so doomed to perpetual escalation." However, shortly before Bruce Bechdel's death, he and his daughter have a conversation in which Bruce confesses some of his sexual history; this is presented as a partial resolution to the conflict between father and daughter.
At several points in the book, Bechdel questions whether her decision to come out as a lesbian was one of the triggers for her father's suicide. This question is never answered definitively, but Bechdel closely examines the connection between her father's closeted sexuality and her own open lesbianism, revealing her debt to her father in both positive and negative lights.
Bechdel describes her journey of discovering her own sexuality: "My realization at nineteen that I was a lesbian came about in a manner consistent with my bookish upbringing." Yet, hints of her sexual orientation arose early in her childhood; she wished "for the right to exchange [her] tank suit for a pair of shorts" in Cannes and for her brothers to call her Albert instead of Alison on one camping trip. Her father also exhibited homosexual behaviors, but the revelation of this made Bechdel feel uneasy. "I'd been upstaged, demoted from protagonist in my own drama to comic relief in my parents' tragedy". Father and daughter handled their issues differently. Bechdel chose to accept the fact, before she had lesbian relationship, but her father hid his sexuality. He was afraid of coming out, as illustrated by "the fear in his eyes" when the conversation topic comes dangerously close to homosexuality.
In addition to sexual orientation, the memoir touches on the theme of gender identity. Bechdel had viewed her father as "a big sissy"" while her father constantly tried to change his daughter into a more feminine person throughout her childhood.
The underlying theme of death is also portrayed. Unlike most young people, the Bechdel children have a tangible relationship with death because of the family mortuary business. Alison ponders whether her father's death was an accident or suicide, and finds it more likely that he killed himself purposefully.
The allusive literary references used in Fun Home are not merely structural or stylistic: Bechdel writes, "I employ these allusions ... not only as descriptive devices, but because my parents are most real to me in fictional terms. And perhaps my cool aesthetic distance itself does more to convey the Arctic climate of our family than any particular literary comparison." Bechdel, as the narrator, considers her relationship to her father through the myth of Daedalus and Icarus. As a child, she confused her family and their Gothic Revival home with the Addams Family seen in the cartoons of Charles Addams. Bruce Bechdel's suicide is discussed with reference to Albert Camus' novel A Happy Death and essay The Myth of Sisyphus. His careful construction of an aesthetic and intellectual world is compared to The Great Gatsby by F. Scott Fitzgerald, and the narrator suggests that Bruce Bechdel modeled elements of his life after Fitzgerald's, as portrayed in the biography The Far Side of Paradise. His wife Helen is compared with the protagonists of the Henry James novels Washington Square and The Portrait of a Lady. Helen Bechdel was an amateur actress, and plays in which she acted are also used to illuminate aspects of her marriage. She met Bruce Bechdel when the two were appearing in a college production of The Taming of the Shrew, and Alison Bechdel intimates that this was "a harbinger of my parents' later marriage". Helen Bechdel's role as Lady Bracknell in a local production of The Importance of Being Earnest is shown in some detail; Bruce Bechdel is compared with Oscar Wilde. His homosexuality is also examined with allusion to Marcel Proust's In Search of Lost Time. The father and daughter's artistic and obsessive-compulsive tendencies are discussed with reference to E. H. Shepard's illustrations for The Wind in the Willows. Bruce and Alison Bechdel exchange hints about their sexualities by exchanging memoirs: the father gives the daughter Earthly Paradise, an autobiographical collection of the writings of Colette; shortly afterwards, in what Alison Bechdel describes as "an eloquent unconscious gesture", she leaves a library copy of Kate Millett's memoir Flying for him. Finally, returning to the Daedalus myth, Alison Bechdel casts herself as Stephen Dedalus and her father as Leopold Bloom in James Joyce's Ulysses, with parallel references to the myth of Telemachus and Odysseus.
The chapter headings, too, are all literary allusions. The first chapter, "Old Father, Old Artificer," refers to line in Joyce's A Portrait of the Artist as a Young Man, and the second, "A Happy Death," invokes the Camus novel. "That Old Catastrophe" is a line from Wallace Stevens's "Sunday Morning," and "In the Shadow of the Young Girls in Flower" is the literal translation of the title of one of the volumes of Marcel Proust's In Search of Lost Time, which is usually given in English as Within a Budding Grove.
In addition to the literary allusions which are explicitly acknowledged in the text, Bechdel incorporates visual allusions to television programs and other items of pop culture into her artwork, often as images on a television in the background of a panel. These visual references include the film It's a Wonderful Life, Bert and Ernie of Sesame Street, the Smiley Face, Yogi Bear, Batman, the Road Runner and Wile E. Coyote, the resignation of Richard Nixon and The Flying Nun.