Public transportation infrastructure is a typical, complex, coupled network that is usually composed of connected bus lines and subway networks. This study proposes an entropy-based node importance identification method for this type of coupled network that is helpful for the integrated planning of urban public transport and traffic flows, as well as enhancing network information dissemination and maintaining network resilience. The proposed method develops a systematic entropy-based metric based on five centrality metrics, namely the degree centrality (DC), betweenness centrality (BC), closeness centrality (CC), eigenvector centrality (EC), and clustering coefficient (CCO). It then identifies the most important nodes in the coupled networks by considering the information entropy of the nodes and their neighboring ones. To evaluate the performance of the proposed method, a bus-subway coupled network in Chengdu, containing 10,652 nodes and 15,476 edges, is employed as a case study. Four network resilience assessment metrics, namely the maximum connectivity coefficient (MCC), network efficiency (NE), susceptibility (S), and natural connectivity (NC), were used to conduct group experiments. The experimental results demonstrate the following: (1) the multi-functional fitting analysis improves the analytical accuracy by 30% as compared to fitting with power law functions only; (2) for both CC and CCO, the improved metric's performance in important node identification is greatly improved, and it demonstrates good network resilience.