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Improving the capacity of wireless networks is critical and challenging. Although wireless standards such as IEEE 802.11 allow the use of multiple channels at the physical layer, current Media Access Control (MAC) and routing protocols of mobile ad hoc networks have mainly been developed to run over one channel. In this paper, we design a unified MAC and routing framework to exploit the temporal and frequency resources to significantly improve the throughput of ad hoc networks. Our joint channel assignment and routing scheme searches for an efficient transmission path, taking into account the constraints due to the limited number of available channels and radio interfaces and the impact of MAC-layer scheduling. Channel maintenance schemes are proposed to adapt the path and channel assignment in response to the changes of network topology and channel condition, as well as feedback from the MAC layer. Given the routing path and channel assignment, our scheduling scheme at the MAC layer explores the resources at the time domain to coordinate transmissions within an interference range to maximize channel usage, reduce channel access competition among nodes assigned to the same channel, coordinate radio interface usage to avoid unnecessary channel switching, and support load balancing. Complemented with the scheduling algorithm, a prioritized transmission scheme is presented to resolve collisions from multiple nodes scheduled to transmit on the same channel in the same time period and to reduce the transmission delay of mission-critical packets and message broadcast, which help further improve network performance. Our simulations demonstrate that our integrated MAC and routing design can efficiently utilize the channel resources to significantly improve the throughput of multichannel multi-interface ad hoc networks.