The bulk complex permittivity of a composite material is calculated analytically. The filler particles are spheroidal and may be coated with a surface layer whose intrinsic material properties differ from those of the core. Making the assumption that the filler particles are arranged on a simple-cubic lattice, interactions between the particles are accounted for by treating each particle mathematically as a multipole source. The coefficients of the multipole expansion, suitably-truncated, are determined by solving a matrix equation obtained by matching with the general solution of Laplace's equation in the interstitial domain, expressed in terms of an expansion in spheroidal harmonics. Matching is carried out at the surface of a representative particle according to electromagnetic continuity conditions. Example calculations demonstrate the effect of varying filler volume fraction, intrinsic material properties, layer thickness, particle shape and frequency. Results are shown to agree with independent work, where available.