Mixtures of ionic surfactants of opposite charge ("catanionic" mixtures) show strongly nonideal behaviors, for example, in terms of evolution of surface tension, critical micelle concentration, or morphology with respect to composition in each surfactant. In several catanionic systems, it has been proposed that the interaction between both surfactants is so strong that lateral phase segregation occurs within bilayers, with crystallites of preferential composition demixing from the excess of the other surfactant. Here, we investigate the temperature-composition phase diagram of the myristic acid/cetyltrimethylammonium mixtures. Combining microcalorimetry, X-ray diffusion, and solid-state deuterium NMR, we demonstrate that no separation is observed in the gel (L-beta) state. The catanionic mixtures therefore behave like two-dimensional solid solutions with a negative azeotrope: the existence of a composition at which a maximum in melting temperature is observed does not imply the existence of a preferential crystal of this composition, but results from the preferential attraction between unlike amphiphilic molecules. Additionally, this study reveals the presence of a so-called intermediate phase, that is, a phase that shows dynamic properties intermediate between that of the L-beta and the L-alpha phases.