In this paper, we propose an intelligent reflecting surface (IRS)-assisted hybrid transmit-receive spatial modulation (HSM) for full-duplex (FD) multi-input multi-output communication, referred to as FD-IRS-HSM. In the proposed FD-IRS-HSM, the FD communication between two users is accomplished with a dedicated IRS for each user. In addition to the conventional data transfer, transmit and receive spatial modulations are simultaneously employed in the transmission by tuning the reflecting elements in the IRS. Further, we characterize the self-interference power, present the theoretical analysis for ergodic capacity and outage probability for the proposed system, and substantiate it with simulation results. We also compare the proposed FD-IRSHSM with closely related works in the literature and demonstrate the outperformance of our proposed system in terms of higher transmission rate and greater flexibility.