The dielectric and electrokinetic properties of aqueous suspensions of vesicles (unilamellar liposomes) are numerically calculated in the 1 Hz to 1 GHz frequency range using a network simulation method. The model consists of a conducting internal medium surrounded by an insulating membrane with fixed surface charges on both sides. Without an applied field, the internal medium is in electric equilibrium with the external one, so that it also bears a net volume charge. Therefore, in the presence of an applied ac field, there is fluid flow both in the internal and in the external media. The obtained results are qualitatively different from those corresponding to suspensions of charged homogeneous particles, mainly due to the existence of an additional length scale (the membrane thickness) and the corresponding dispersion mechanism, charging of the membrane. Because of this dispersion, the shapes of the spectra change with the size of the particles (at constant xi potential and particle radius to Debye length ratio) instead of merely shifting along the frequency axis. A comparison between the numerical results and those obtained using approximate analytical expressions shows deviations that are, in general, sufficiently large enough to show the necessity to use numerical results in order to interpret broad frequency range dielectric and electrokinetic measurements of vesicle suspensions.