Hydrogen doped amorphous silicon carbide layers were grown by radiofrequency magnetron sputtering technique using a gas mixture of Ar and H2. The film thickness, the refractive index and the absorption coefficient of the films were obtained by means of optical transmittance in the UV/VIS/NIR spectral region. In order to study the effect of the hydrogen doping on the optical properties of the layers, a constant hydrogen flux was used during the deposition process. The optical bandgap was calculated using different models of the fundamental absorption region. First, a good linear dependency in the Tauc-plot was observed from which the bandgap could be calculated. Second, the E04 iso-absorption optical gap was extracted. Finally, the Urbach rule was used to determine the Urbach energy and the Urbach focus of the films. In order to correlate the bandgap variation with further thermal annealing temperatures and the out diffusion of hydrogen, the vibrational properties of the different bonds were studied through FTIR measurements. Such spectra present the Si-H, the Si-CHn and Si-C bonds. Finally, the material exhibited an enhancement of the optical bandgap when doped with hydrogen. And moreover, a critical annealing temperature is found for which the bandgap reached its maximum value in both cases, doped and undoped samples.