In this paper we present model calculations of the deformation of a glassy polymer film supported by a plastically deforming metal substrate. The focus is on the resulting roughening of the free polymer surface. In the calculations a mixed-mode rate independent cohesive zone has been employed as the interface between the metal and the polymer. The mechanical behavior of the polymer is characterized by an elastic regime, a softening regime and finally a hardening regime. Above the yield point of the polymer shear bands occur that transfer the evolving roughness of the deforming metal through the polymer coating. It turns out that in this regime the resulting rms roughness at the free polymer surface may be higher than that of the underlying metal substrate. For this to occur the thickness of the coating must be higher than the correlation length of the rough metal substrate.