A theoretical study of the multi-coupling flexural and longitudinal waves that propagate in a periodic dual-beam-type waveguide with structural connection branches is conducted. The analytical equations of the transfer matrix method are derived for the wave transmission with consideration given to the fully flexural and longitudinal motions that are tri-coupled at each connection. Based on this transfer matrix method, numerical calculation is performed to investigate the characteristic wave-types that propagate in a semi-infinite periodic structure. The complex wave-coupling phenomena in the periodically connected dual-beam waveguide are then analyzed numerically. Remarkably, it is found that three symmetric and three antisymmetric types of characteristic coupled waves propagate in a periodic structure. The numerical results show that the energy contribution of the coupled waves with respect to the source excitation depends on the forbidden band of the wave-types and on the energy ratios and combination of wave-types. This study promotes the fundamental understanding and prediction of coupled acoustic waves in multi-layered frame structures. The long-term significance is that it may lead to a more effective control method for structure-borne sound transmission in a multi-layered coupling structure.