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The performance of multi-channel multi-radio (MC-MR) wireless mesh networks (WMNs) can be improved significantly with the increase in number of channels and radios. Despite the availability of multiple channels in several of the current wireless standards, only a few of them are non- overlapping and many channels are partially overlapped. In this paper, we formulate the joint channel assignment and flow allocation problem for MC-MR WMNs as a mixed integer linear program (MILP). Unlike most of the previous studies, we consider the case of using both non-overlapped and partially overlapped channels. We consider an objective of maximizing aggregate end-to-end throughput and minimizing queueing delay in the network, instead of the sum of link capacities, since the traffic characteristics of a multihop WMN are quite different from a single hop wireless network. Our formulation takes into consideration several important network parameters such as the transmission power of each node, path loss information, signal to interference plus noise ratio at a node, and frequency response of the filters used in the transmitter and receiver. We show by simulations that our MILP formulation makes efficient use of the spectrum, by providing superior channel assignments and flow allocations with the addition of partially overlapped channels, without the use of any additional spectrum.