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The aggregate capacity of wireless mesh networks can be increased by the use of multiple frequency channels and multiple network interface cards in each router. Recent results have shown that the performance can further be increased when both non-overlapped and partially overlapped channels are being used. In this paper, we propose a linear model for a joint channel assignment, interface assignment, and scheduling design. We propose the channel overlapping matrix and mutual interference matrices to model the non-overlapped and partially overlapped channels. Since the model is formulated as a linear mixed-integer program with a few integer variables, the computation complexity is low and it is feasible for implementation. Simulation results show that the aggregate network capacity increases by 90% when all partially overlapped channels within the 802.11b frequency band are being used.