First-principles calculations based on density functional theory are performed on graphene/BN and BN bilayers to investigate the effect of the strain on their energy gaps. For the graphene/BN bilayer, the bands have characteristic graphenelike features with a small band gap at K. Application of strain modulates the band gap, whose magnitude depends on the strength of interaction between constituent monolayers. For the BN bilayer, on the other hand, a large band gap is predicted, which remains nearly the same for small strains. The increased inhomogeneity in charge density of different carbon sublattices due to a stronger interplanar interaction is the cause of the predicted variation in the band gap with strains applied along the perpendicular direction in the graphene/BN bilayer.