We study an optomechanical system in which a microwave field and an optical field are coupled to the same mechanical oscillator. We explore the feasibility of using these mechanical oscillators to store quantum mechanical states and to transduce states between optical and microwave electromagnetic oscillators with special consideration given to the effect of mechanical decoherence. Besides being of fundamental interest, this coherent quantum state transfer could also have important practical implications in the field of quantum information science because it allows one to utilize the advantages while overcoming the intrinsic limitations of both platforms. We discuss several state transfer protocols and study their transfer fidelity using a full quantum mechanical model and implementing quantum state diffusion in order to describe the dissipative effects. We find that a state transfer fidelity of 95\% can be achieved for parameters realizable with current experimental technology.