First-principles calculations based on all-electron density functional theory are performed on hydrogenated graphene/boron nitride (BN) bilayer and graphene/BN multilayers to exploit the effects of the heterogeneous interface and external bias voltage on controlling their electronic properties. After hydrogenation, the emerging of the dipoles at the interface induced by the charge transfer between the graphene and the BN layer introduces a built-in potential difference, which plays a critical role in determining the band gaps of the resulting system. Tuning this internal potential difference through changing the number of BN layers or an external bias allows continuous modulation of the band gaps and leads to a linear transition from semiconductors to metals.