Omnidirectional light propagation in a realistic superlattice is investigated. This work complements two previous articles [Phys. Rev. E 59, 3624 (1999); 61, 5802 (2000)] that analyzed the cases of transverse electric (TE) and transverse magnetic (TM) polarization modes, respectively, of the dielectric superlattice modeled by means of Dirac delta functions. We present a quantitative analysis of the transmission functions, the band structures, the equifrequency surfaces, and the photon density of states (PDOS) for both TE and TM modes of the real superlattice without any approximations on the given dielectric function profiles. One of the advantages is that the Brewster effect can be manifested via our approach. In addition, the modes corresponding to TM evanescent waves that are absent from the Dirac comb model can be predicted. Finally, the exact PDOS of the realistic superlattice for the TE and TM modes can be obtained, respectively. These results are relevant to the spontaneous emission by an atom or to dipole radiation in one-dimensional periodic structures.