With recent advances in wireless technology, the importance of the capability to use multiple transmission rates and multiple radios has been widely recognized. In this paper, multi-rate and multi-radio (MR2) characteristics are exploited to improve end-to-end transmission delay for reliable multicasts. To achieve this goal, maximum potential rate based on multiple rates and radio based transmission delay with a different number of available radios are investigated in the construction of multicast routes. Multi-rate multi-radio on-demand multicast routing protocol (MR2_ODMRP), a protocol that makes ODMRP suitable for a MR2 environment, is proposed. An integer linear programming model is proposed to obtain the optimal tree as well as the rate and radios at each node of the tree for each multicast service. The solution is employed to evaluate the performance of the MR2_ODMRP. From the simulation, it is shown that the MR2_ODMRP produces nearly optimal solutions even in environments with a large number of nodes. It outperforms the ODMRP in wireless mesh networks. The end-to-end transmission delay is improved by a factor of four compared to the ODMRP.