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Abstract Semiconductor heterojunctions are ubiquitous components of modern electronics. Their properties depend crucially on the band alignment at the interface, which may exhibit straddling gap (type-I), staggered gap (type-II) or broken gap (type-III). The distinct characteristics and applications associated with each alignment make it highly desirable to switch between them within a single material. Here we demonstrate an electrically tunable transition between type-I and type-II band alignments in MoSe₂/WS₂heterobilayers by investigating their luminescence and photocurrent characteristics. In their intrinsic state, these heterobilayers exhibit a type-I band alignment, resulting in the dominant intralayer exciton luminescence from MoSe₂. However, the application of a strong interlayer electric field induces a transition to a type-II band alignment, leading to pronounced interlayer exciton luminescence. Furthermore, the formation of the interlayer exciton state traps free carriers at the interface, leading to the suppression of interlayer photocurrent and highly nonlinear photocurrent-voltage characteristics. This breakthrough in electrical band alignment control, interlayer exciton manipulation, and carrier trapping heralds a new era of versatile optical and (opto)electronic devices composed of van der Waals heterostructures.