By using first-principles simulations, we investigate the interaction of silicene and germanene with various non-metallic substrates. We first consider weak van der Waals interactions between the 2D layers and dichalcogenide substrates, like MoX 2 (X=S, Se, Te). The buckling of the silicene or germanene layer is correlated to the lattice mismatch between the 2D material and the MoX 2 template. The electronic properties of silicene or germanene on these different templates then largely depend on the buckling of the 2D material layer: highly buckled silicene or germanene on MoS 2 are predicted to be metallic, while low buckled silicene on MoTe 2 is predicted to be semi-metallic, with preserved Dirac cones at the K points. We next study the covalent bonding of silicene and germanene on (0001) ZnS and ZnSe surfaces. On these substrates, silicene or germanene are found to be semiconducting. Remarkably, the nature and magnitude of their energy band gap can be controlled by an out-of-plane electric field.