We investigate the transmittivity spectra, fields, and energy distribution of the electromagnetic eigenwaves propagating in a one-dimensional (1D) dielectric photonic crystal [(TiO₂/SiO₂)^NAl₂O₃]^M with two periods formed by unit cells TiO₂/SiO₂ and (TiO₂/SiO₂)^NAl₂O₃. Spectra of TE- and TM-modes depend on the geometric parameters of the structure and undergo modifications with the change in the period numbers, layer thicknesses, and incidence angle. Special attention is paid to the applicability of the hybrid effective medium approximation comprising the long-wave approximation and two-dimensional (2 × 2) transfer matrix method. We demonstrate spectral peculiarities of the bi-periodic structure and also show the differences between the band gap spectra of the bi-periodic and ternary 1D dielectric photonic crystals. The presented photonic crystal structure can find its applications in optoelectronics and nanophotonics areas as omnidirectional reflectors, optical ultra-narrow bandpass filters, and antireflection coatings.