This study investigates the application of a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided medium-Earth-orbit (MEO) satellite network for providing both global positioning services and communication services in the urban canyons, where the direct satellite-user links are obstructed. Superposition coding (SC) and successive interference cancellation (SIC) techniques are utilized for the integrated navigation and communication (INAC) networks, and the composed navigation and communication signals are reflected or transmitted to ground users or indoor users located in urban canyons. To meet diverse application needs, navigation-oriented (NO)-INAC and communication-oriented (CO)-INAC have been developed, each tailored according to distinct power allocation factors. We then proposed two algorithms, namely navigation-prioritized-algorithm (NPA) and communication-prioritized-algorithm (CPA), to improve the navigation or communication performance by selecting the satellite with the optimized position dilution of precision (PDoP) or with the best channel gain. The effectiveness of the proposed STAR-RIS-aided INAC network is quantified by analyzing the positioning error for navigation services and by evaluating communication performance through achievable ergodic rate metrics. Our satellite selection approach indicates that: the positioning services at the urban canyon users can be completed with the aid of STAR-RIS. 2) Additionally, it is observed that while a single STAR-RIS array can extend the navigational link, it fails to serve users in indoor scenarios, highlighting a limitation in the current system design.