A range of novel two-dimensional materials have been actively explored for More Moore and More-than-Moore device applications because of their ability to form van der Waals heterostructures with unique electronic properties. However, most of the reported electronic devices exhibit insufficient control of multifunctional operations. Here, we leverage the band-structure alignment properties of narrow-bandgap black phosphorus and large-bandgap molybdenum disulfide to realize vertical heterostructures with an ultrahigh rectifying ratio approaching 106 and on-off ratio up to 107. Furthermore, we design and fabricate tunable multivalue inverters, in which the output logic state and window of the mid-logic can be controlled by specific pairs of channel length and, most importantly, by the electric field, which shifts the band-structure alignment across the heterojunction. Finally, high gains over 150 are achieved in the inverters with optimized device geometries, showing great potential for future logic applications.