Using density functional theory calculations with van der Waals correction, we show that the electronic properties (band gap and carrier mobility) and work functions of graphane/fully hydrogenated hexagonal boron nitride (G/fHBN) heterobilayers can be favorably tuned via heteronuclear dihydrogen bonding (C-HH-B and C-HH-N) and an external electric field. Our results reveal that G/fHBN heterobilayers have different direct band gaps of ∼1.2 eV and ∼3.5 eV for C-HH-B and C-HH-N bonds, respectively. In particular, these band gaps can be effectively modulated by altering the direction and strength of the external electric field (E-field), and correspondingly exhibit a semiconductor-metal transition. The conformation and stability of G/fHBN heterobilayers show a strong dependence on the heteronuclear dihydrogen bonding. Fantastically, these bonds are stable enough under a considerable external E-field as compared with other van der Waals (vdW) 2D layered materials. The mobilities of G/fHBN heterobilayers we predicted are hole-dominated, reasonably high (improvable up to 200 cm(2) V(-1) s(-1)), and extremely isotropic. We also demonstrate that the work function of G/fHBN heterobilayers is very sensitive to the external E-field and is extremely low. These findings make G/fHBN heterobilayers very promising materials for field-effect transistors and light-emitting devices, and inspire more efforts in the development of 2D material systems using weak interlayer interactions and electric field control.