The dielectric properties of complex plasma containing either metal or dielectric spherical inclusions (macroparticles, dust) are investigated. We focus on surface plasmon resonances on the macroparticle surfaces and their effect on electromagnetic wave propagation. It is demonstrated that the presence of surface plasmon oscillations significantly modifies plasma electromagnetic properties by resonances and cutoffs in the effective permittivity. This leads to related branches of electromagnetic waves and to the wave band gaps. The results are discussed in the context of dusty plasma experiments.