We have developed a fit method that allows detailed analysis of complicated ellipsometric spectra, such as those of thick (~10µm) multilayer structures found in modern integrated optics devices. Ellipsometry should be the natural choice for thorough nondestructive characterisation of those heterostructures, but extraction of the required parameters is often impracticable by common approaches. Our fit procedure is based in spline parametrisations of the unknown optical functions and is applicable to materials either with a smooth optical response or displaying sharp electronic transitions in the analysed energy range. We have applied our method to characterise PECVD-grown non-stoichiometric silicon oxides (SiOx) and thick waveguide structures based on these materials.