Answer
The bright fringes are very, very close to being midway between the dark fringes, but are not EXACTLY there.
Work Step by Step
Equations 35.4 and 35.5 gives the angle at which bright and dark fringes occur, respectively. As m increases, the angle changes in a complicated, nonlinear way and the bright fringes are very, very close to being midway between the dark fringes, but are not EXACTLY there.
However, for small angles, or when the screen distance is much greater than the slit separation and much greater than the distance between fringes, it is an excellent approximation to assume that the bright fringes are halfway between the dark ones.