We demonstrate locally coherent heteroepitaxial growth of silicon carbide (SiC) on diamond, a result contrary to current understanding of heterojunctions as the lattice mismatch exceeds $20%$. High-resolution transmission electron microscopy (HRTEM) 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 realising 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 heterostructure formation with large lattice mismatch.