We demonstrate locally the coherent formation of silicon carbide (SiC) on diamond, a rare example of heteroepitaxy with a lattice mismatch that exceeds 20%. High-resolution transmission electron microscopy confirms the quality and atomic structure near the interface. Guided by molecular dynamics simulations, a theoretical model is proposed for the interface wherein the large lattice strain is alleviated via point dislocations in a two-dimensional plane without forming extended defects in three dimensions. The possibility of realizing heterojunctions of technologically important materials such as SiC with diamond offers promising pathways for thermal management of high-power electronics. At a fundamental level, the study redefines our understanding of SiC and diamond heteroepitaxy and furthers our understanding of large lattice mismatched interfaces.