In this paper we present formulas for the transmission coefficient in multibarrier heterostructures when taking into account the space-dependent electron effective mass and the coupling between components of the motion of an electron in directions parallel and perpendicular to the interfaces. We find that the coupling leads to a decrease of the effective barrier height seen by the electron. The numerical calculations are carried out for the double-and triple-barrier heterostructures consisting of GaAs/Ga12xAlxAs. Our results show that the coupling effect leads not only significantly to a shift of resonant peaks toward the low-energy region, but also causes the broadening of resonant peaks and the reduction of the peak-to-valley ratio in the transmission spectrum. The coupling becomes more pronounced for higher-lying resonant states. In addition, the variation of the coupling strength with the concentration x of Al is also investigated.