We have used neutron reflection and phase contrast microscopy to investigate the morphology and surface topology of thin films of nearly symmetric (f=0.55) and asymmetric (f=0.77), poly (ethylene-propylene)-poly (ethylethylene) (PEP-PEE) diblock copolymers (f being the PEP volume fraction) and have identified three important differences in their ordering properties. First, annealed films of the asymmetric diblocks do not form the lamellar microstructure found in symmetric diblocks; their structure can instead be modeled in terms of the hexagonal packing of PEE cylinders observed in bulk small-angle neutron scattering measurements. However, the cylinders show in-plane distortions, which we interpret in the context of nonintegral layering. These distortions are amplified at the surfaces where the PEE assumes lamellarlike form. Second, as-cast films of the asymmetric diblock are characterized by a microstructure lacking long-range order, pinned between strongly segregated PEE at both surfaces. These films can be equilibrated through annealing, leading to the well-ordered structures described earlier. The changes with annealing are surprising given that both PEP and PEE are well above their glass transitions at room temperature. Finally, the block asymmetry and the associated cylindrical structure in the interior are also manifested in the surface topology. Thin films of asymmetric PEP-PEE are smooth on a macroscopic scale unlike their symmetric counterparts, which form islands on the surface to accommodate films of nonintegral lamellar thicknesses.