We consider a simple model for the dielectric response of a water-rich surfactant sponge phase (L3), in which an insulating bilayer separates two continuous brine domains (''in'' and ''out''). Experiments of Vinches, Coulon and Roux (J. Phys. II, 4 (1994) 1165) show for high salt concentrations a bimodal relaxation. We associate their higher-frequency mode with behaviour on the sale of a single pore of the sponge, and the lower-frequency one with fluctuations in the ''in/out'' order parameter. For a perfect bilayer, we predict a divergence of the real part of the relative permittivity at the in/out symmetry breaking transition. This is consistent with the extremely high values (epsilon congruent-to 10(7)) observed experimentally in some high salt samples.