We introduce a theoretical scheme to study defect energy levels and band alignments at semiconductor-oxide interfaces. The scheme relies on hybrid functionals to overcome the band gap underestimation typically achieved with semilocal density functionals. For atomically localized defects, the more accurate description achieved with, hybrid functionals does not lead to significant shifts of the charge transition levels, provided these levels are referred to a common reference potential. This result effectively decouples the shifts of the band edges with respect to the defect levels. We also show that relative shifts of conduction and valence band edges as determined by exact nonlocal exchange. lead to band offsets in excellent agreement with experimental values for several semiconductor-oxide interfaces. The proposed scheme is illustrated through a series of applications, including the dangling bond defects in silicon and germanium, the charge state of the O-2 molecule during silicon oxidation, and the oxygen vacancy in Si-SiO2 HfO2 stacks.