In this paper we investigate the coupling of flexural and longitudinal wave motions in a waveguide with structural side branches attached at regular intervals. The analysis is based on periodic structure theory, and considers wave transmission in a fully tricoupled and semidefinite periodic assembly of beam-type elements or plane-wave transmission for normal incidence in a similar plate assembly. Receptances of a composite periodic element with offset resonant beams are derived and used for computing the frequency-dependent propagation constants of three coupled wave types as well as the distribution of motion displacements in each wave type. This is used for calculating the spatial variation of the forced harmonic responses of a semi-infinite periodic structure to point excitations by a longitudinal force and by a moment. Numerical simulations reveal the complicated wave coupling phenomena, which are clarified by calculating the ratio of flexural and longitudinal kinetic energies in the wave-carrying component for each wave type. In contrast to a corresponding, but uncoupled, system with significant broadband attenuation of flexural waves, the numerical results further show that the flexural-longitudinal wave coupling in a system with resonant side branches results in a highly enhanced wave transmission with very little attenuation from element to element.