The mechanical properties of heterophase interfaces are critically important for the behaviour of graphene-reinforced composites. In this work, the structure, adhesion, cleavage and sliding of heterophase interfaces, formed between a ZrB2 matrix and graphene nanosheets, are systematically investigated by density functional theory, and compared to available experimental data. We demonstrate that the surface chemistry of the ZrB2 matrix material largely shapes the interface structures (of either Zr-C-Zr or B-C-B type) and the nature of the interfacial interaction. The Zr-C-Zr interfaces present strong chemical bonding and their response to mechanical stress is significantly influenced by graphene corrugation. In contrast B-C-B interfaces, interacting through the relatively weak π-π stacking, show attributes similar to 2D materials heterostructures. Our theoretical results provide insights into the interface bonding mechanisms in graphene/ceramic composites, and emphasize the prospect for their design via interface engineering enabled by surface contacts.