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In the presence of dispersion and dissipation, we deduce a modified plane wave expansion method to calculate photonic bands in 2-D honeycomb lattice photonic crystals (PCs) composed of plasma-coated layers. A linearization technique of the generalized eigenvalue problem for a complex matrix of wave expansion is used to obtain the photonic band structures. In the transverse magnetic mode, when plasma-coating thickness increases to a critical value, most of the dielectric-plasma (DP) photonic bands are the same as photonic bands generated by pure plasma cylinders. This property provides us a way to replace plasma PCs with DP PCs that save energy and materials. In the transverse electric mode, multiflatbands below the plasma frequency also occupy a large frequency range when the plasma coating is sufficiently large. Given that these multiflatbands are caused by surface plasmon polaritons, the region of flatbands depends not on the geometry of the photonic lattice but on the filling factor of the plasma coating. The numerical results validate the correctness of our prediction.