We propose and evaluate vertical hot-electron terahertz (THz) detectors based on black-As1−xPx/graphene/black-As1−yPy (b-AsP/G/b-AsP) heterostructures. The operation of these detectors is associated with the thermionic emission of the electrons heated in the graphene layer (G-layer) by incoming THz radiation stimulating the electron injection from the emitter, i.e., with the hot-electron bolometric mechanism. The combination of the effective electron heating in the G-layer with the features of the b-As1−xPx and b-As1−yPy band structures with a proper relation between the b-P fractions, x and y (x ≥ y), might result in the high photoconductive gain and detector responsivity of the proposed detectors. As discussed, these detectors can surpass the similar bolometric detectors based on graphene-based heterostructures with relatively high energy barriers for the electrons and holes in the G-layers and the bolometric detectors based on III-V quantum wells.