We present a new model to analyze dielectric spectroscopy measurements on charged lamellar systems, with the following improvements with respect to the hitherto available models: (i) it does not rely on the hypothesis of local electro-neutrality, and allows to treat the salt-free case; (ii) the chemical exchange governing the partition between free and bound ions is properly taken into account; (iii) a fully analytical solution is provided. The variation of the frequency-dependent dielectric permittivity with both thermodynamic and kinetic characteristics of the free-bound ion equilibrium is presented. In particular, the relative weights of both relaxation modes (exchange and transport), and their characteristic frequencies are discussed. This study opens the way to the analysis of systems for which the usual models are irrelevant, such as salt-free clay gels or membranes.