We have investigated the solidification microstructures of the non-equiatomic and equiatomic V-Nb-Mo-Ta-W alloys, which are one of the first refractory high entropy alloys, and found intriguing dual body-centered cubic (BCC) microstructures. There were two issues to be addressed in these alloys: an unidentified strengthening mechanism and intense microsegregation in the as-cast state. We determined that the as-cast microstructure of the non-equiatomic V₁₄Nb₁₉Mo₂₀Ta₂₄W₂₃ and V₂₂Nb₂₄Mo₂₄Ta₂₄W₁₀ alloys consist of two BCC phases with different lattice constants, and that the equiatomic alloy of the V-Nb-Mo-Ta-W system consists of two BCC phases with different compositions but the same lattice constants. The two BCC phases form lattice-matched interfaces, suggesting that precipitation-hardening with high lattice-matching can be one of the reasons for the excellent high-temperature mechanical properties of this alloy system. In addition, we also found that the alloys that were poor in V and Nb, and rich in Ta and W compositions solidified without precipitating of secondary BCC phases. The alloys in this compositional range have partition coefficients of the elements closer to 1 than those with near-equiatomic compositions.