As various platforms are being developed in quantum information science, measures to interconnect disparate quantum systems are necessary. Superconducting qubits for quantum computation operate at gigahertz frequencies and heavily depend on microwave technologies. On the other hand, quantum communications are realized with optical techniques utilizing visible and infrared lasers. In order to connect quantum computers and construct a quantum network, intermediate systems that convert quantum states between microwave and optical frequencies are required. Recently, optomechanical systems have attracted great attention as potential applications for coherent quantum conversion. A mechanical oscillator with a high quality factor can couple to both microwave and optical fields simultaneously and mediate coherent conversions between them. As a first step, we focus on coupling a nanoscale silicon-nitride membrane with a superconducting microwave resonator. Physically, two heterogeneous resonators interact each other by the small capacitance formed between them. Constructing the combined circuit requires a multistep fabrication process and precise alignment. The integrated system can be simplified as coupled harmonic oscillators and described by number operators with a coupling constant. The hybrid device provides an excellent opportunity to study quantum electrodynamics involving acoustics.