© 2020 American Physical Society. Transition metal dichalcogenide (TMD) bilayers have recently emerged as a robust and tunable moiré system for studying and designing correlated electron physics. In this Rapid Communication, by combining a large-scale first-principles calculation and continuum model approach, we provide an electronic structure theory that maps long-period TMD heterobilayer superlattices onto diatomic crystals with cations and anions. We find that the interplay between the moiré potential and Coulomb interaction leads to filling-dependent charge transfer between different moiré superlattice regions. We show that the insulating state at half filling found in recent experiments on WSe2/WS2 is a charge-transfer insulator rather than a Mott-Hubbard insulator. Our work reveals the richness of simplicity in moiré quantum chemistry.