Dielectric relaxation in binary mixtures containing particles or lamellae with complex geometry has been simulated within the quasielectrostatic approximation by a three-dimensional finite-difference method. The method was tested using simple models corresponding to water-in-oil (W/O) and oil-in-water (O/W) emulsions with volume fraction P up to 0.5. The dielectric spectra calculated by the finite difference method agreed with those expected from Wagner's equation at P <= 0.3 and approached those from Hanai's equation at P > 0.4. This method was applied to more complicated binary mixtures of oil and water: a bicontinuous cubic structure, a suspension of particles with projections, and a planar bilayer with a rippled or interdigitated interface. The bicontinuous phase that is supposed to appear near the transition between W/O and O/W emulsions showed dielectric properties similar to those of the O/W emulsion. The undulation of the particle surface and the interface of the planar bilayer affected all parameters of dielectric relaxation, especially the relaxation intensity. (c) 2005 Elsevier Inc. All rights reserved.