Van der Waals heterostructures, a new class of materials made of a vertically selective assembly of various 2D monolayers held together by van der Waals forces, have attracted a great deal of attention due to their promise to deliver novel electronic and optoelectronic properties that are not achievable by using individual 2D crystals. Using density functional theory (DFT), it is revealed that van der Waals heterostructures composed of monolayers of hexagonal boron nitride (h-BN) and the latest P allotrope blue phosphorus (blue phosphorene, BlueP) forms a straddling type I band offset for which the band edges exclusively belong to BlueP. This feature enables h-BN to act as a protective coating material to resolve the air instability of BlueP. Furthermore, substitutional doping of C into h-BN (h-BCN) at a suitable concentration induces h-BCN–BlueP into staggered type II band offset. The type II band alignment triggered by the intensified built-in electric field across the sheets implies improved carrier mobility and the suppressed recombination of photogenerated hole pairs. These major benefits can pave the way for the potential functionality of h-BCN–BlueP to be exploited for efficient photovoltaic devices.