We study symmetric and nearly symmetric diblock copolymers confined to thin films of thickness L, where L is the equilibrium bulk lamellar period. The film surfaces have opposite preferences for the polymer species; this results in frustration. We use the Scheutjens-Fleer method to calculate the free energies of several parallel (with respect to the film surfaces), perpendicular, and mixed perpendicular morphologies as a function of the preferential wetting strengths of the polymer species at the film surfaces. When the film surface is highly preferential, the perpendicular morphology adopts a novel structure not seen in bulk diblock copolymer melts. In addition, when the diblock copolymers are slightly asymmetric, a mixed perpendicular morphology, in which half of the film resembles the perpendicular morphology and half of the film resembles a parallel morphology, can be stable. We calculate a phase diagram in the plane of the preferential wetting strengths at the two surfaces and find that the perpendicular morphology or the mixed perpendicular morphology is the equilibrium morphology in a significant portion of the plane. This is in contrast to the simple, strong segregation limit, flat interface theory, which essentially predicts that only parallel morphologies should be observed in (equilibrium) L-thick films.