It has been shown that intraflow network coding (NC) can improve the multicast throughput in single-channel single-rate wireless mesh networks. Most existing studies focus on developing a practical intraflow NC multicast protocol. With the rise of wireless products supporting multirate multichannel communications nowadays, it has become increasingly important to improve the NC gain by utilizing multiple bit rates and nonoverlapping channels, but new challenges have also arisen due to various tradeoffs. In a multirate multichannel multihop network, overhearing opportunities and bandwidth utilization are highly correlated to the selection of the channel and rate, which in turn determines the achievable throughput of multicast with intraflow NC. Specifically, wireless nodes can transmit at higher bit rates over orthogonal channels to increase the forwarding throughput, but the strategy reduces overhearing opportunities and the coding gain in multicast with intraflow NC. To achieve the best tradeoff between the given two aspects, we formulate a new optimization model called multirate multichannel multicast with intraflow NC (RCMNC), which solves the joint channel assignment, rate selection, and flow allocation problems for multihop intraflow NC multicast. We then reformulate the primal problem as the Lagrangian dual problem and propose an algorithm to approximate the solution of the dual problem in polynomial time. Simulation results show that, by assigning a suitable rate and channel to each network interface, the multicast throughput with intraflow NC under RCMNC is up to 3.3 times higher than that achieved by the existing approach in a multirate multichannel wireless mesh network.