The strong coupling constant g(hb)B(C)(PS)B(C)(V) is calculated using the three-point QCD sum-rule method. We use correlation functions to obtain these strong coupling constants with contributions of both B-C(PS) and B-C(V) mesons as off-shell states. The contributions of two gluon condensates as a radiative correction are considered. The results show that g(hb)B(C)(PS)B(C)(V) = 8.80 +/- 2.84 GeV-1 and g(hb)B(C)(V)B(C)(PS) = 9.34 +/- 3.12 GeV-1 in the B-C(PS) and B-C(V) off-shell state, respectively.