A mixed Reed-Muller and Dual Reed-Muller(RM-DRM) logic model is proposed to achieve a more compact logic representation for a Boolean function and improve the quality of the synthesized circuit. The mixed RM-DRM logic representation for a Boolean function is constructed by using Hamming distance based cube cover partitioning, and is optimized by using EXORCISM-4 tool on the basis of duality principle. Being used as a structural representation model, the mixed RM-DRM logic is applied to reversible circuit synthesis. The experimental results show that compared to the Reed-Muller logic model, the mixed RM-DRM logic model can reduce the quantum cost of the synthesized reversible circuits for some functions, and can reduce the average quantum cost of the synthesized reversible circuits for the 134 functions from RevLib benchmark suite.