We measured the dielectric function of Ge1-yCy and Ge-rich Si1-x-yGexCy alloys from 1.6 to 5.2 eV using spectroscopic ellipsometry. These alloys were grown by molecular beam epitaxy at 600 degrees C on (001) Si substrates. Analytic lineshapes fitted to numerically calculated derivatives of their dielectric functions determined the critical-point parameters of the E-1, E-1 + Delta(1), E-0', and E-2 transitions. The critical-point energies of the Ge1-yCy alloys were found to be indistinguishable from those of bulk Ge. This indicates that the presence of C in these alloys has no detectable influence on the band structure. The amplitude of the ellipsometric spectra is much lower than for bulk Ge, which can be attributed to surface roughness and explained within the framework of the Kirchhoff theory of diffraction or using effective medium theory. The degree of surface roughness indicated by optical measurements was verified by atomic force microscopy.