Using first principles calculations, we investigate the electronic and magnetic properties of BNC biribbons, a laterally-heterostructured nanoribbon constructed by joining a graphene nanoribbon (GNR) and a BN nanoribbon (BNNR) with zigzag edges. We find that the spin-polarization and electronic structures of the biribbons can be well-tuned by changing the width of the GNR, undergoing manifold transitions from semiconducting to half-metal and ferromagnetic metal. The critical points of GNR width to induce the transitions depend on the interface type (B/C or C/N) rather than the BNNR width. The ground states of metallic BNC biribbons are spin-polarized, forming non-zero magnetic moments. The tunable electronic structures and ferromagnetic ground states make the BNC biribbons promising candidate nanomaterials for building nanoscaled spintronic devices.