We present first-principles calculations of structural and electronic properties of heterova-lent SiC/GaN, SiC/AIN, and isovalent AIN/GaN heterostructures that are grown pseudo-morphically on (001) or (110) SiC substrates. For the polar interfaces, we have investigated reconstructed stoichiometric interfaces consisting of one and two mixed layers with lateral c(2 × 2), 2 × 1, 1 × 2, and 2 × 2 arrangements. The preferred bonding configurations of the reconstructed interfaces are found to be Si-N and Ga-C. With respect to vacuum, the valence band maximum is found to be highest in SiC and lowest in A1N. In these systems, the valence band offsets deviate substantially from the transitivity rule and depend sensitively on the microscopic details of the interface geometry. The SiC/AIN and AIN/GaN heterostructures are predicted to be of type I, whereas SiC/GaN heterostructure can be of type I or II.