We present a strong stretching theory model for microphase segregation of AB + AC block copolymer. blends in which the B and C segments possess strongly attractive (hydrogen bonding) interactions. In microphase separated morphologies, we demonstrate that the attraction between the B and the C segments causes a bending force toward the A layer's. Such bending forces may induce transitions from lamellar and A-majority cylindrical morphologies in the pure component systems to "inverted" cylindrical and spherical morphologies in blends in which the B and C segments constitute the matrix phase. Similar driving forces may also drive transitions from A-majority spherical phases in pure component systems to highly asymmetric lamellar morphologies in blends. The predictions of our model are in excellent agreement with the trends observed in recent experimental results.