Two-dimensional materials, such as graphene and monolayer hexagonal BN (h-BN), are attractive for demonstrating fundamental physics in materials and potential applications in next-generation electronics. Atomic sheets containing hybridized bonds involving elements B, N and C over wide compositional ranges could result in new materials with properties complementary to those of graphene and h-BN, enabling a rich variety of electronic structures, properties and applications. Here we report the synthesis and characterization of large-area atomic layers of h-BNC material, consisting of hybridized, randomly distributed domains of h-BN and C phases with compositions ranging from pure BN to pure graphene. Our studies reveal that their structural features and bandgap are distinct from those of graphene, doped graphene and h-BN. This new form of hybrid h-BNC material enables the development of bandgap-engineered applications in electronics and optics and properties that are distinct from those of graphene and h-BN.