Using first-principles calculations, we show that the recently synthesized two-dimensional (2D) van der Waals layered material indium selenide (InSe) nanosheets can serve as a suitable substrate for silicene and germanene, which form commensurate and stable silicene/InSe (Si/InSe) and germanene/InSe (Ge/InSe) heterolayers (HLs). The buckled honeycomb geometries and Dirac-cone-like band structures of silicene and germanene are well preserved in these HLs. The interaction between silicene (or germanene) and the InSe substrate opens up a band gap of 141 meV (or 149 meV) at the Dirac points, while electron effective masses (EEM) remain as small as 0.059 and 0.067 times the free-electron mass (m0). The band gap and the EEM of the HLs can be further modulated effectively by applying an external electric field or strain. These features are attributed to the built-in electric field due to the interlayer charge transfer of the HLs which breaks the equivalence of the two sublattices of silicene and germanene. Multilayer (ML) InSe substrates have also been considered. We also proposed a parallel plate capacitor model to describe the interaction between silicene (or germanene) and the InSe substrate as well as the electronic band structure modification in response to an external field. This work is expected to offer an ideal substrate material for the growth of silicene and germanene and a promising van der Waals (vdW) layered heterostructure for electronic devices.