Reflectance measurements under normal incidence of light and variable angle spectroscopic ellipsometry (SE) studies are applied for characterizing hexagonal GaN films grown by molecular beam epitaxy on both GaAs (111)B and 6H-SiC substrates. A comparison of the reflectance above the band gap with model calculations for a smooth film yields definitely the root mean square surface roughness. By analyzing the envelopes of the reflectance spectra, the influence of a buffer layer and/or a non-abrupt substrate/film interface is verified and qualitative conclusions about the interface properties are deduced which are emphasized by transmission electron microscopy studies. On this basis a suitable model for data fitting is established which contains only a small number of parameters to be adjusted. From the fit, the complex refractive index versus photon energy as well as the thicknesses of the active layer and the interlayers are obtained. A meticulous analysis of the SE data below the band gap shows that from those studies the extraordinary refractive index of hexagonal GaN can be determined for the first time.