We report on the optical bandgap engineering of sputtered hydrogenated amorphous silicon carbide (a-SiC:H) thin films under different hydrogen dilution conditions during the deposition process and after post-deposition annealing treatments. The Tauc-gap and Urbach energy are calculated from ultraviolet-visible optical transmittance measurements. Additionally, the effect of the thermal annealing temperature on the hydrogen out-diffusion is assessed through infra-red absorption spectroscopy. A new model for the optical absorption of amorphous semiconductors is presented and employed to determine the bandgap as well as the Urbach energy from a single fit of the absorption coefficient. This model allowed the discrimination of the Urbach tail from the Tauc region without any external bias. Finally, the effect of the hydrogen dilution on the band-edge and the Urbach focus is discussed. © 2016 IOP Publishing Ltd.