Using molecular dynamics simulations and a model AlN-GaN interface, we demonstrate that the interfacial thermal resistance R(K) (Kapitza resistance) between a substrate and thin film depends on the thickness of the film and the film surface roughness when the phonon mean free path is larger than film thickness. In particular, when the film (external) surface is atomistically smooth, phonons transmitted from the substrate can travel ballistically in the thin film, be scattered specularly at the surface, and return to the substrate without energy transfer. If the external surface scatters phonons diffusely, which is characteristic of rough surfaces, R(K) is independent of film thickness and is the same as R(K) that characterizes smooth surfaces in the limit of large film thickness. At interfaces where phonon transmission coefficients are low, the thickness dependence is greatly diminished regardless of the nature of surface scattering. The film thickness dependence of R(K) is analogous to the well-known fact of lateral thermal conductivity thickness dependence in thin films. The difference is that phonon-boundary scattering lowers the in-plane thermal transport in thin films, but it facilitates thermal transport from the substrate to the thin film.