Beyond the study of individual materials, their interfaces and arising functionality are crucial enablers of fundamental science and technological progress. Recently, the arena of two-dimensional (2D) materials was extended to so-called non-van der Waals (non-vdW) compounds derived from strongly bonded non-layered bulk crystals. These nanosystems have advantageous active surfaces and thus now complement – through their chemically bonded heterostructure (HS) interfaces – the established space of weakly interacting vdW HSs. Here, we study a wide range of 55 candidate non-vdW HSs with extensive density functional calculations and find that the resulting interfacial chemical hybridization and bonding is the key factor determining their electronic and magnetic properties. It gives rise to the formation of unique hybrid interface bands, strong magnetic coupling, and substantial electronic as well as magnetic moiré surface property modulations upon twisting. Our work thus provides a valuable platform for charting the new interface class of non-vdW HSs.