A Newton-Kantorovitch numerical algorithm is proposed for obtaining both the refractive index profile and the thickness of inhomogeneous films from multiple angle of incidence ellipsometry data. The reliability and effectiveness of the algorithm are tested for a number of model inhomogeneous transparent coatings with different refractive index profiles and degrees of inhomogeneity. It is demonstrated that the retrieved profiles and thickness are close to the model ones, even when the sensitivity of the ellipsometric angle T to the film inhomogeneity is low.