The wireless mesh networks (WMN) has attracted significant interests as a next-generation broadband wireless network to provide ubiquitous wireless access for broadband services. Especially with incorporating multiple orthogonal channels and multiple directional antennas into the WMN, each node can communicate with its neighbor nodes simultaneously without interference between them. In addition, due to directional antennas, the interference range of each transmission can be significantly reduced and we can further utilize the frequency separation. Hence, we can improve the throughput of the WMN significantly with multiple orthogonal channels and multiple directional antennas. In this paper, we study a joint channel and flow assignment problem for the WMN with multiple channels and multiple directional antennas. We first formulate an optimization problem as a mixed integer optimization problem that aims at maximizing the network utility. Since it is inherently hard to solve the mixed integer optimization problem, we propose a heuristic algorithm to solve the problem. The simulation results show our heuristic algorithm provides a reasonable performance in terms of the network utility compared to its upper bound.