A parametric description of the dielectric function of Pd thin films with thicknesses between 10 and 30 nm is reported. These films were grown at room temperature on amorphous quartz substrates by electron beam evaporation, with a base pressure of 7.0×10(-7) mbar. By using nonpolarized normal incident light, transmission spectra were measured for wavelengths between 240 and 1050 nm. Inversion of the spectra by means of a projected gradient method enables us to obtain the mean dielectric function of the Pd grains in the films. We follow the Brendel-Bormann model to describe the frequency dependence of the dielectric function, with the plasma frequency, collision frequency, and screening factor as parameters in the free electron term. The contributions of bound electrons and their interband transitions, described in terms of Lorentz oscillators, involve the resonance frequencies, decay times, strengths, and Gaussian widths as parameters of the model. All these parameters have been optimized from the Pd grains' dielectric function, which fits the transmission spectra. A similar procedure was followed for Pd films exposed to a hydrogen atmosphere close to one bar. Thus, the dielectric functions of palladium and palladium hydride can easily be calculated through spectral ranges covering near-ultraviolet, visible, and near-infrared wavelengths. This can be used to model the behavior of nano-sized structures in which palladium particles or thin films are exposed to hydrogen pressures close to one bar.