We calculate charge transition levels of various defects at the SiC/SiO2 interface within a scheme based on hybrid density functionals, which accurately reproduce the involved band gaps and band offsets. The defect levels are first evaluated in bulk models of the interface components and then aligned with respect to the interface band diagram through the use of a model interface showing good structural and electronic properties. Interface-specific polarization effects are evaluated separately through classical electrostatics. We considered carbon-related defects involving single atoms and dimers in both the crystalline SiC substrate and the amorphous SiO2 oxide. Our investigation also comprises oxygen-and hydrogen-related defects, including the Si-Si bond (O vacancy), the Si-2-C-O structure, the peroxy linkage, and the hydrogen bridge (Si-H-Si). Among the defects studied, the Si-2-C-O structure represents the best candidate for the high defect density measured near the conduction band of SiC.