Recent research has demonstrated the feasibility of full-duplex (FD) communication over the same frequency channel. This capability, facilitated by new self-interference suppression techniques, has great potential to increase the network capacity. However, exploiting FD in the context of a multi-user, multi-channel network is still being debated. This paper focuses on the channel access issue and presents a novel multi-channel MAC (MMAC) protocol for wireless ad hoc networks with FD and orthogonal frequency-division multiple access (OFDMA) capabilities. Through these capabilities, a node can simultaneously carry out multiple transmissions and/or receptions over the same or different channels. In our MMAC protocol, a pair of nodes negotiate data channels, transmission rates, transmission powers, and transmission modes (e.g., FD or half-duplex) in a distributed manner so that their spectral usages are minimized while their rate demands are still met. Extensive ns3 simulations show that our MMAC protocol increases the end-to-end network goodput by up to 150% and decreases the end-to-end delay by up to 300% compared with an OFDMA-based protocol without FD.