Real-time spectroscopic ellipsometry (RTSE) has been applied to characterize composition depth-profiles in compositionally-graded amorphous silicon-carbon alloy (a-Si1-xCx:H) thin films, prepared using continuous variations in the flow ratio z(t) = [CH4]/{[SiH4] + [CH4]} during r.f. plasma-enhanced chemical vapor deposition (PECVD). In order to calculate the dielectric functions of a-Si1-xCx:H alloys for any value of x, a new parameterization of the measured dielectric functions was established using the recently-derived Tauc-Lorentz (T-L) model. This model is found to provide improved fitting of the measured dielectric functions of a-Si1-xCx:H over the analyzed energy region of 2.2 < E < 4.2 eV, in comparison to previous parameterization schemes. Applying the T-L parameterization, the depth-profiles in the C-content were then analyzed using a virtual interface approximation. For several a-Si1-xCx:H graded layers having triangular variations in the C-content (0 < x < 0.24) over 25-130 Angstrom thick layers, we found very good agreement between the analyzed depth-profiles and those predicted from z(t) based on individually-deposited samples. In the depth-profile of the thinnest C-graded layer (similar to 25 Angstrom), monolayer depth resolution was evident with an average compositional uncertainty of +/- 0.009.