This paper presents a cross-layer approach for enabling high-throughput reliable multicast in multi-hop wireless mesh networks. The building block of our approach is a multicast routing metric, called the expected multicast transmission count (EMTX). EMTX is designed to capture the combined effects of MAC-layer retransmission-based reliability, wireless broadcast advantage, and link quality awareness. The EMTX of single-hop transmission of a multicast packet from a sender is the expected number of multicast transmissions (including retransmissions) required for its next-hop recipients to receive the packet successfully. We formulate the EMTX-based multicast problem with the objective of minimizing the sum of EMTX over all forwarding nodes in the multicast tree, aiming to reduce network bandwidth consumption while ensure high end-to-end packet delivery ratio for the multicast traffic. We provide rigorous mathematical formulations and methods to find near-optimal solutions of the problem computationally efficiently. We present centralized and distributed algorithms, and demonstrate their effectiveness in tackling the EMTX-based multicast problem with a combination of theoretical and numerical results. Simulation experiments show that, in comparison with two baseline approaches, EMTX-based multicast routing reduces the number of hop-by-hop transmissions per packet by up to 40 percent and yet improves the multicast throughput by up to 24 percent.