We investigated the zone structure peculiarities and the photonic density of states (PDS) of the eigen polarizations (EPs) in the system composed of a stack of layers of a cholesteric liquid crystal (CLC) and an isotropic medium. The problem was solved by Ambartsumian's layer addition modified method. The influence of the CLC sublayer thicknesses and the thicknesses of the isotropic media layers on the reflection an PDS spectra of the system is investigated.