We use polymer reference interaction site model (PRISM)-based density functional theory (DFT) to study the structures and morphologies of block copolymer thin films. The polymers are modeled as freely jointed chains, allowing numerical solution of the nonlinear DFT equations. The use of PRISM with DFT allows the inclusion of compressibility and local packing effects due to the finite size of the monomers. We also employ a pseudo-arclength continuation algorithm to locate phase transitions and new morphologies. We study symmetric diblock copolymers confined between two parallel surfaces which both attract one component of the diblock, for two different values of AB segregation strength and for various surface interactions. The predicted equilibrium morphologies are in good qualitative agreement with previous self-consistent field calculations and are consistent with experiment. We are able to resolve the detailed packing structure near the surfaces. We find that packing effects enhance the stability of the perpendicular morphologies.