Using first principles, classical potentials, and elasticity theory, we investigated the structure of a semiconductor/semiconductor interface with a high lattice mismatch, SiC/Si(001). Among several tested possible configurations, a heterostructure with (i) a misfit dislocation network pinned at the interface and (ii) reconstructed dislocation cores with a carbon substoichiometry is found to be the most stable one. The importance of the slab approximation in first-principles calculations is discussed and estimated by combining classical potential techniques and elasticity theory. For the most stable configuration, an estimate of the interface energy is given. Finally, the electronic structure is investigated and discussed in relation with the dislocation array structure. Interface states, localized in the heterostructure gap and located on dislocation cores, are identified.