Microwave transmission and reflection in a periodic superconductor/ dielectric film multilayer structure in the mixed state are theoretically calculated. It is based on the model of vortex dynamics of a type-II superconductor in the mixed state as well as the transfer matrix method in a stratified medium. We have made some numerical analyses in the microwave transmission and reflection as functions of temperature, dielectric thickness, and number of periodicity as well. The results indicate that the temperature-dependent reflection can be enhanced by increasing the number of periodicity. In addition, both microwave reflection and transmission will be reduced if the thickness of dielectric film is increased.