To leverage the scalability limits of traditional routing/multicasting for mobile ad hoc networks, a typical approach adopts two-tier architectures by selecting a fraction of the network hosts as backbone hosts (BHs). BHs are responsible for managing the architectures and performing routing/multicasting; thus, the proper way of selecting BHs is crucial to two-tier architectures. Once a host with low stability (i.e., high mobility) to the neighborhood hosts is selected as a BH, the architecture may become fragile, and the performance may dramatically decline. In this paper, a distinct strategy is proposed to select stable BHs. The Global Positioning System (GPS) is used to estimate the amount of remaining connection time for two neighboring hosts, and with its aid, stable BHs with longer remaining connection time to the other hosts are selected. In addition, a new multicast protocol is proposed based on the selected stable BHs to select stable multicast routes. A stable route is a route that is available for a longer time. Simulation results show that the proposed protocol has shorter transmission latency, shorter more stable multicast routes, lower overhead, more stable attachment of multicast members to BHs, and higher receiving data packet ratios than other existing two-tier multicast protocols.