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In this paper, we propose a multi-band medium access control (MAC) protocol for an infrastructure-based network with an access point (AP) that supports In-Band full-duplex (IBFD) and multiuser transmission to multi-band-enabled stations. The Multi-Band Full Duplex MAC (MB-FDMAC) protocol mainly uses the sub-6 GHz band for control-frame exchange, transmitted at the lowest rate per IEEE 802.11 standards, and uses the 60 GHz band, which has significantly higher instantaneous bandwidth, exclusively for data-frame exchange. We also propose a selection method that ensures fairness among uplink and downlink stations. Our result shows that MB-FDMAC effectively improves the spectral efficiency in the mmWave band by 324%, 234%, and 189% compared with state-of-the-art MAC protocols. In addition, MB-FDMAC significantly outperforms the combined throughput of sub-6 GHz and 60 GHz IBFD multiuser MIMO networks that operate independently by more than 85%. In addition, we study multiple network variables such as the number of stations in the network, the percentage of mmWave band stations, the size of the contention stage, and the selection method on MB-FDMAC by evaluating the change in the throughput, packet delay, and fairness among stations. Finally, we propose a method to improve the utilization of the high bandwidth of the mmWave band by incorporating time duplexing into MB-FDMAC, which we show can enhance the fairness by 12.5%and significantly reduces packet delay by 80%.