Here we demonstrate by theoretical analysis a novel way to enhance the omnidirectional total-reflection wavelength range in one-dimensional photonic bandgap material by using a ternary periodic structure (i.e., three material layers constituting a period of the lattice). The omnidirectional total reflection range using a binary $(\mathrm{Ba}{\mathrm{F}}_2∕\mathrm{Pb}\mathrm{S})$ periodic structure was enhanced by $108\mathrm{nm}$ when the structure was modified by sandwiching a thin layer of $\mathrm{Zr}{\mathrm{O}}_2$ between every two layers, constituting a period of the lattice. A shift of the omnidirectional range toward higher wavelengths was also observed. When the sandwiched layer was $\mathrm{Ce}{\mathrm{F}}_3$ , the enhancement in the range was $120\mathrm{nm}$ . As the sandwiched layer is very thin, there will not be any significant increase in the size of the reflector, contrary to the case of heterostructured photonic crystals (PCs) where two or more PCs are clubbed together to achieve enhancement.