The surface morphology of thin bilayer polymer films on top of glass substrates was investigated. The bilayer consists of a blend film of protonated and deuterated polystyrene and an underlying deuterated polystyrene film. Choosing the thickness of the top film larger than 8 times and smaller than 2 times the radius of gyration of the chains enables the determination of film thickness and confinement effects. With diffuse neutron scattering at grazing incidence in the region of total external reflection, a depth sensitivity and a contrast even at the internal polymer-polymer interface was achieved. The underlying film is conformal to the substrate, and depending on the thickness of the top film two different types of roughness correlations are observed. Thin confined films nestle to the underlying polymer films, while the stiffness of thicker bulky films provides an independent morphology. In both cases, annealing above the glass-transition temperature yields an interdiffusion at the internal polymer-polymer interface, and the polymer-air surface remains essentially unchanged with respect to roughness correlations.