The exciton-phonon coupling has been studied in InxGa1-xN/GaN and GaN/AlxGa1-xN multiple quantum wells (MQWs) and compared with that in InxGa1-xN and GaN epilayers. Phonon replicas with up to four phonons can be well resolved only in the alloy regions of the MQWs (InxGa1-xN or AlxGa1-xN) and was independent of the structure (well or barrier), while no phonon replicas of the exciton transitions were observed for the free-exciton transitions in the GaN and the localized exciton transitions in the InxGa1-xN epilayers. It thus suggests that the symmetry properties of MQWs, which modifies the phonon dispersion relation, together with alloy disorder are responsible for the enhanced exciton-phonon interaction in III-nitride MQW. The coupling constant S of the exciton-phonon interaction is extracted for an InxGa1-xN/GaN and GaN/AlxGa1-xN MQW, and is found to be S = 0.802 and 0.556, respectively. The implications of the modified exciton-phonon coupling in MQWs in terms of understanding the fundamental physics of this system as well as practical device applications are discussed.