A model layered superionic conductor, which is composed of alternating layers of superionic conductors and ionic crystal, is described on the basis of a continuum model. Using linear-response theory, the dielectric function and ionic conductivity of the system are obtained as a function of frequency, wave number, and the distance between the adjacent layers. It is shown that these response functions satisfy a sum rule. The longitudinal collective modes obtained from the dielectric function are classified into two kinds of modes: the acoustic-phonon mode and the coupled optical-phonon--ionic-plasma mode. The ionic-plasma mode has changed from the three-dimensional to the two-dimensional plasma mode with the increase of the distance between layers. Also in the strong-coupling limit where the distance is small enough the ionic-plasma mode has shown two phases: bulklike and acousticlike plasma modes.