Using first principle calculations, we have studied the structural and electronic properties of two dimensional bilayers of indium and gallium chalcogenides. With density functional theory corrected for van der Waals interactions, the different modes of stacking were investigated in a systematic way, and several of them were found to compete in energy. Then, their band structures were obtained with the GW approximation and found to correspond to indirect bandgap semiconductors with a small dependency on the mode of stacking. Finally, by analysing the electron density, it appeared that GaSe-InS is a promising system for electron-hole separation. Published by AIP Publishing.