Photonic band structures explored in the past 12 years were mainly fabricated from dielectric materials, typically used in the semiconductor technology. However, we foresee novel applications and interesting possibilities by incorporating the photonic crystals concept into superconducting devices. In this paper, we study the band structure of a non-dissipative superconductor-dielectric superlattice using the two-fluid model. We apply the dispersion relations in both layers of the superlattice to the transcendental equation for a double-layer superlattice, from which we compute the bandgap structure for the dielectric-superconducting superlattice. Computation results show the existence of dispersion-curve splitting similar to the phonon-polariton case in addition to the low-frequency gap similar to the plasma-frequency gap. The polariton gap size is characterized by polarization and the penetration depth, and highly dependent on temperature at the vicinity of superconducting transition temperature. Our analysis shows that the properties of this material structure may have application in optical region if extremely low relaxation time superconductor is used. This may be an asset for superconducting electronics-photonics integration.