Electrochemical impedance spectra of composite materials contain information on the topological arrangement, volume fraction, and shape of particles, as well as the dielectric properties of the matrix and particles. The objective of this study is to investigate how these parameters affect the dielectric spectrum and what reliable information can be extracted from experimental data. The main attention was focused on systems with dielectric behavior similar to that of human blood. Mostly plasma and erythrocytes determine the dielectric properties of whole blood. Erythrocytes suspended in plasma can be considered as three-phase systems with single-shelled particles. A theoretical approach based on the effective medium theory is developed for calculating the effective permittivity and conductivity of three-phase composites at a wide frequency range (from 0 to 1 GHz). A finite-difference method is applied to model three-dimensional periodic structures. A special case of two-phase materials is used to demonstrate the influence of the shape and arrangement of particles on dielectric properties. Theoretical and numerical approaches are applied to two-phase composites with spherical, spheroidal and biconcave particles and are compared with each other and with published data. It is shown that two-phase composites exhibit only β-dispersion. In contrast to the quasi-static limit, the wide-bandwidth impedance spectroscopy makes it possible to distinguish between disordered and regular arrangements of spheroidal and biconcave particles. The results can be used to analyze the dielectric properties of blood, which is very promising for various medical applications. This study of two-phase composites can be further extended to three-phase composites.