Band-to-band transition energy parameters for single-crystal actinide samples of uranium oxide and thorium oxide were determined and compared using spectroscopic ellipsometry and critical-point dielectric function analyses. Spectroscopic ellipsometry measurements from the near-infrared to the vacuum ultraviolet spectral region were used to determine the dielectric functions of uranium oxide and thorium oxide. The critical-point structure is similar between UO2 and ThO2 but strongly blue shifted for ThO2. We find bandgap energies of 2.1 eV and 5.4 eV for UO2 and ThO2, respectively