Hafnium oxide (HfO2 or hafnia) holds promise as a high-index dielectric in optical devices and thermal barrier coatings, because of its transparency over a broad spectrum (from the ultraviolet to the mid-infrared) and chemical and thermal stability at high temperatures. In the present work, thin hafnia films of thicknesses from about 180 to 500 nm are deposited on Si substrates using reactive magnetron sputtering. The crystalline structure and surface topography are characterized by X-ray diffraction and atomic force microscopy, respectively. The optical and radiative properties of the film–substrate composites are measured at room temperature using spectroellipsometry and Fourier-transform infrared spectrometry. The optical constants are obtained from about 0.37 to 500 μm by fitting suitable models to the experimental results. Optical properties and dielectric function modeling are discussed with correlation to both film thickness and surface roughness. It is found that a single-oscillator dielectric-function model can describe radiative properties from about 1 to 20 μm. By combining Cauchy's formula (for the visible and near-infrared regions) with a multiple-oscillator Lorentz model (for the far-infrared region), a dielectric function is obtained for the HfO2 films that is applicable from the visible to the far-infrared.