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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 is a charge-transfer insulator rather than a Mott-Hubbard insulator. Our work reveals the richness of simplicity in moiré quantum chemistry.