We study high-throughput multicast solutions for wireless mesh networks (WMN). Two techniques in WMN design are considered for combating wireless bandwidth limitations and wireless interference, respectively: introducing multiple mesh gateways and exploiting the diversity of wireless channels. We target a cross-layer solution that jointly (a) selects appropriate channels for each mesh node to use, at judiciously tuned power, and (b) computes the optimal multicast flows associated with the channel assignment. Our solution is obtained by first formulating the WMN multicast problem into a mathematical program, and then designing an iterative primal-dual optimization framework for it based on Lagrange relaxation and primal problem decomposition. Solution algorithms for the decomposed sub-problems are designed to complete the solution. In particular, a progressive channel assignment heuristic is introduced at the MAC/PHY layer. Through extensive simulations, we demonstrate the effectiveness of the proposed solution framework and the sub-problem heuristics. In particular, a throughput improvement of up to 100% is observed when compared to straightforward approaches of utilizing multiple wireless channels for mutlicast routing.