A mixed amphiphilic system composed of the anionic surfactant Aerosol OT (AOT), in water forming a lamellar phase, to which is added a neutral noninteracting polymer, poly(N,N-dimethylacrylamide), is studied experimentally by SAXS, H-2 NMR, and microscopy, in a range of surfactant and polymer compositions. Addition of the polymer produces a decrease in the lamellar spacing, the decrease by the polymer being almost twice that produced by an equal volume of AOT. Microscopy reveals heterogeneity, but no macroscopic phase separation occurs. H-2 NMR detects that on increasing the polymer concentration some water is in an isotropic environment. It is inferred that the presence of the polymer induces a microscopic phase separation into a polymer-rich isotropic phase and a surfactant-rich lamellar phase, and this is tested theoretically by calculating the osmotic pressures in these two phases. In the lamellar phase, the effect of electrostatic, undulation, van der Waals, and hydration forces on the AOT bilayer is considered; in the isotropic phase, the osmotic contribution of the polymer is considered. These two pressures correlate well, supporting theoretically the hypothesis of the two phases in equilibrium.