We investigate different aspects of the absolute photonic band gap (PBG) formation in two-dimensional photonic structures consisting of rods covered with a thin dielectric film. Specifically, triangular and honeycomb lattices in both complementary arrangements, i.e., air rods drilled in silicon matrix and silicon rods in air, are studied. We consider that the rods are formed of a dielectric core (silicon or air) surrounded by a cladding layer of silicon dioxide (SiO2), silicon nitride (Si3N4), or germanium (Ge). Such photonic lattices present absolute photonic band gaps, and we study the evolution of these gaps as functions of the cladding material and thickness. Our results show that in the case of air rods in dielectric media the existence of dielectric cladding reduces the absolute gap width and may cause complete closure of the gap if thick layers are considered. For the case of dielectric rods in air, however, the existence of a cladding layer can be advantageous and larger absolute PBG’s can be achieved.