We consider a wireless communication system, where a transmitting source is assisted by both a reconfigurable intelligent reflecting surface (IRS) and a decode-and-forward half-duplex relay (hybrid IRS-relay scheme) to communicate with a destination receiver. All devices are equipped with multiple antennas, and transmissions occur in two stages. In stage 1, the source splits the transmit message into two sub-messages, transmitted to the destination and the relay, respectively, using block diagonalization to avoid interference. Both transmissions will benefit from the IRS. In stage 2, the relay re-encodes the received sub-message and forwards it (still through the IRS) to the destination. We optimize power allocations, beamformers, and configurations of the IRS in both stages, in order to maximize the achievable rate at the destination. We compare the proposed hybrid approach with other schemes (with/without relay and IRS), and confirm that high data rate is achieved for the hybrid scheme in case of optimal IRS configurations.