The model of Forouhi and Bloomer (FB) for the optical properties of amorphous semiconductors is modified in order to describe more accurately the dispersion of the optical constants observed for amorphous carbon (a-C) and amorphous hydrogenated carbon (a-C:H) thin firms. The FB model represents the optical absorption as the product of a lineshape function and a joint density of states function, which is derived by assuming the condition and valence bands to be parabolic and separated by an energy gap within which there are no allowed electronic states. Two modifications to this model are discussed to address the cases of non-parabolic bands and/or electron energy levels in the energy gap. These modified parametric models are then fit to a large number of a-C and a-C:H film optical constant spectra, and results are presented which indicate that non-parabolicity of the conduction and valence bands is the most important correction to the standard FB model required to describe a-C:H thin films. The modified model incorporating non-parabolic bands is shown to fit a broad range of both a-C and a-C:H spectra very well, and provides useful information about the optical absorption process and physical properties of the films.