Systematic density functional theory (DFT) computations revealed the existence of considerable C-H center dot center dot center dot F-C bonding between the experimentally realized graphane and fluorographene layers. The unique C-H center dot center dot center dot F-C bonds define the conformation of graphane/fluorographene (G/FG) bilayer and contribute to its stability. Interestingly, G/FG bilayer has an energy gap (0.5 eV) much lower than those of individual graphane and fluorographene. The binding strength of G/FG bilayer can be significantly enhanced by applying appropriate external electric field (E.-field). Especially, changing the direction and strength of E-field can effectively modulate the energy gap of G/FG bilayer, and correspondingly causes a semiconductor-metal transition. These findings open new opportunities in fabricating new electronics and opto-electronics devices based on G/FG bilayer, and call for more efforts in using weak interactions for band structure engineering.