In-band full duplex (IBFD) systems require promising resource allocation (RA) strategies to fully exploit the available time-frequency resources. Furthermore, the acquisition of channel state information and signal reception in IBFD systems are significantly impacted by insufficient self-interference cancellation (SIC), impeding the applications of IBFD in practical wireless systems. Multicarrier-division duplex (MDD), which benefits low-budget SI mitigation in digital domain and flexible subcarrier assignment, is expected to be a promising transitional technique from half-duplex (HD) to IBFD. Hence, to demonstrate the advantages of MDD over HD, this paper first compares the upper bound performance of MDD and HD by applying unfair greedy RA. Then, considering a more complicated application scenario of the millimeter-wave (mmWave) with hybrid beamforming, we propose the RA optimization with the quality of service (QoS) constraints on both downlink (DL) and uplink (UL) mobile stations (MSs). To solve this non-convex RA problem, we divide it into a suboptimal subcarrier allocation problem, which is solved by the proposed improved fair greedy (IFG) algorithm, and a convex power allocation problem. Furthermore, we design two general hybrid precoder based on matrix factorization and direct approach, and a combiner having high SIC capability. Our results show that the proposed RA algorithm is capable of achieving the performance near the upper bound achieved by the unfair greedy algorithm, while concurrently guaranteeing the proportional fairness among all DL/UL MSs. The performance of the two precoding schemes is depended on the number of radio frequency chains supported. Finally, with appropriate antenna deployment, the proposed SIC algorithm is able to provide sufficient SI mitigation, and furthermore, can be implemented without impacting the RA operation.