Infrared to vacuum-ultraviolet spectroscopic ellipsometry and far-infrared optical Hall-effect measurements are applied to conclude on successful p-type doping of InN films. A representative set of In-polar Mg-doped InN films with Mg concentrations ranging from 1.2×1016 cm−3 to 3.9×1021 cm−3 is investigated. The data are compared and discussed in dependence of the Mg concentration. Differences between n-type and p-type conducting samples are identified and explained. p-type conductivity in the Mg concentration range between 1.1×1018 cm−3 and 2.9×1019 cm−3 is indicated by the appearance of a dip structure in the infrared spectral region related to a loss in reflectivity of p-polarized light as a consequence of reduced LO phonon plasmon coupling, by vanishing free-charge carrier induced birefringence in the optical Hall-effect measurements, and by a sudden change in phonon-plasmon broadening behavior despite continuous change in the Mg concentration. By modeling the near-infrared-to-vacuum-ultraviolet ellipsometry data, information about layer thickness, electronic interband transitions, as well as surface roughness is extracted in dependence of the Mg concentration. A parameterized model that accounts for the phonon-plasmon coupling is applied for the infrared spectral range to determine the free-charge carrier concentration and mobility parameters in the doped bulk InN layer as well as the GaN template and undoped InN buffer layer. The optical Hall-effect best-match model parameters are consistent with those obtained from infrared ellipsometry analysis.