Optical microscopy, neutron reflectivity, and small angle neutron scattering studies were used to investigate the structure of thin films of symmetric diblock copolymers of P(dS-b-MMA) as the interactions between the copolymer and the substrate were changed in a systematic manner. In cases where there was a strong preferential segregation of one of the components to the substrate, the lamellar microdomains were oriented parallel to the film surface. However, on a nearly neutral substrate, a mixed morphology was found where the lamellae adjacent to the free surface are oriented parallel to the plane of the film, while the lamellae adjacent to the substrate are oriented normal to the plane of the film.