Two-dimensional heterostructures are an emerging class of materials for novel applications because of extensive engineering potential by tailoring intriguing properties of different layers as well as the ones arised from their interface. A systematic investigation of mechanical, electronic and optical properties of possible heterostructures formed by bilayer structures graphene-like ZnO and MgO monolayers is presented. Different functionality of each layer makes these heterostructures very appealing for device applications. ZnO layer is convenient for electron transport in these structures, while MgO layer improves electron collection. At the outset, all of the four possible stacking configurations across the heterostructure are mechanically stable. In addition, stability analysis using phonon dispersion reveals that the AB stacking formed by placing the Mg atom on top of the O atom of the ZnO layer is also dynamically stable at zero temperature. Henceforth, we have investigated the optical properties of these stable heterostructures by applying many-body perturbation theory within the framework of GW approximation and solving the Bethe-Salpeter equation. It is demonstrated that strong excitonic effects reduce the optical band gap to the visible light spectrum range. These results show that this new 2D form of ZnO/MgO heterostructures open an avenue for novel optoelectronic device applications.