We develop the device models for the far-infrared interband photodetectors (IPs) with the graphene-layer (GL) sensitive elements and the black Phosphorus (b-P) or black-Arsenic (b-As) barrier layers (BLs). These far-infrared GL/BL-based IPs (GBIPs) can operate at the photon energies ℏ Ω smaller than the energy gap, ΔG, of the b-P or b-As or their compounds, namely, at ℏ Ω≲2Δ G/3 corresponding to the wavelength range λ≳(6-12) μm. The GBIP operation spectrum can be shifted to the terahertz range by increasing the bias voltage. The BLs made of the compounds b-AsxB1-x with different x, enable the GBIPs with desirable spectral characteristics. The GL doping level substantially affects the GBIP characteristics and is important for their optimization. A remarkable feature of the GBIPs under consideration is a substantial (over an order of magnitude) lowering of the dark current due to a partial suppression of the dark-current gain accompanied by a fairly high photoconductive gain. Due to a large absorption coefficient and photoconductive gain, the GBIPs can exhibit large values of the internal responsivity and dark-current-limited detectivity exceeding those of the quantum-well and quantum-dot IPs using the intersubband transitions. The GBIPs with the b-P and b-As BLs can operate at longer radiation wavelengths than the infrared GL-based IPs comprising the BLs made of other van der Waals materials and can also compete with all kinds of the far-infrared photodetectors.