We present a molecular dynamics investigation of the cross-plane thermal conductivity of superlattices using the non-equilibrium molecular dynamics method. The purpose is to investigate the influence of the interfaces, which is expected to be important in those nanostructures where the superlattice period is smaller than the phonon mean free path. In contrast to previous studies, more realistic interfaces are considered: interfacial roughness is modeled using atomic rectangular islands and interdiffusion is taken into account. It is shown that thermal conductivity is very sensitive to the detailed interfacial shape and to the presence of interdiffusion. This may be relevant to recent experiments.