Heterostructures are often expected to be of enhanced electronic properties compared with homogeneous ones. Valuable experimental efforts have been devoted to the fabrication of graphene/hexagonal boron nitride (hBN) lateral heterostructures. It has been shown that abrupt interface between graphene and hBN could form in a controllable manner at the atomic scale. We thus investigate the electronic properties of such new hybrid structures by systematically considering possible interface configurations. Our results obtained with density-functional theorem reveal that interface has significant impact on electronic properties. Specifically, for heterostructures with a zigzag type of interface, electronic states are found to be spin-polarized, and a half-metallic phase is identified when the graphene domain is terminated with zigzag edges. For heterostructures with an armchair type of interface, electronic states display a robust semiconducting behavior. The novelty and diversity in electronic properties have implications for the design of new atomic devices in two dimensions based on lateral heterostructures.