The interface roughness of Cu2O films produced by thermal oxidation of Cu was studied by spectroscopic elastic light scattering and atomic force microscopy. No correlation could be found between the roughness of the two interfaces, although the amplitude and the length scale of the roughness changed in the same way with film thickness for both interfaces. Both interfaces were found to have a fractal dimension of two. A first order perturbation theory was used to analyse the light scattering data; theory and experiment are in good agreement within the limits of the theory.