This paper considers the reliable multicast transport protocols used in hybrid networks that include wired and wireless networks and transparent proxy servers. We present four analytic performance models of two extreme reliable multicast transport protocols, sender-initiated and receiver-initiated, and supported and unsupported by transparent proxy servers are considered in each reliable multicast protocol. We analyze the throughputs of these four different models mathematically. Numerical results show that transparent proxy servers give good effects to overall performance. Furthermore, the receiver-initiated reliable multicast supported by transparent proxy servers gives better performances of total throughput than sender-initiated reliable multicast supported by transparent proxy servers. We provide efficiency criterion of the optimal number of transparent proxy servers for each protocol under varying wireless loss probabilities. Numerical results are verified by simulations.