The van der Waals heterostructure (vdWH) has attracted widespread attention as a unique structure for future electronic and optoelectronic devices. In this paper, we constructed the ZnO-SeMoS and ZnO-SMoSe vdWHs and systematically investigated their electronic structures and band alignments considering vertical strain and external electric field effects. It is found that the ZnO-SeMoS and ZnO-SMoSe vdWHs both exhibit type-II band alignment with indirect band gaps of 1.31 and 0.63 eV respectively, depending on the interface characteristics. What's more, the band alignment of these two heterostructures can be tuned to type I or type III, and their band gap can be modified to direct feature by applying vertical strain and an electric field. The results reveal that ZnO/MoSSe vdWHs have promising potential in multi-functional nanodevices, and provide a way to modify the electronic properties of Janus-based heterojunctions using interface characteristics.