Band offsets at semiconductor-oxide interfaces are determined through a scheme based on hybrid density functionals, which incorporate a fraction alpha of Hartree-Fock exchange. For each bulk component, the fraction alpha is tuned to reproduce the experimental band gap, and the conduction and valence band edges are then located with respect to a reference level. The lineup of the bulk reference levels is determined through an interface calculation, and shown to be almost independent of the fraction alpha. Application of this scheme to the Si-SiO2, SiC-SiO2, and Si-HfO2 interfaces yields excellent agreement with experiment.