We apply positron annihilation spectroscopy to study thermally oxidized and reoxidized 4H- and 6H-SiC. The SiC/SiO2 interface is found to contain a high density of open-volume defects. The positron trapping at the interface correlates with the charge of the interface determined by capacitance-voltage analysis. For oxides grown on n-SiC substrates, the positron annihilation characteristics at these defects are nearly indistinguishable from those of a silicon/oxide interface. These results suggest that at least a part of the defects at the SiC/oxide interface are similar to those at the Si/oxide interface. We infer that the observed open-volume defects are on the oxide side of the interface and possibly consist of Si vacancies in the oxide near the interface.