We Study the confinement of a hydrophilic polymer (polyethylene glycol or PEG) between the bilayers of the zwitterionic surfactant tetradecyldimethyl aminoxide (C(14)DMAO). Small angle X-ray scattering and electron microscopy experiments show that the polymer modifies the physical properties of the lyotropic smectic (L-alpha) phase. The observed effects are similar to those reported for anchored hydrophobically-modified polymers, indicating a strong interaction between PEG and the C(14)DMAO bilayers. Self-diffusion experiments performed in the lyotropic sponge (L-3) phase show that the polymer adsorbs onto the surfactant membranes. This adsorption explains earlier observations: high polymer concentrations decrease the Gaussian rigidity of the membranes and a vesicular phase is stabilized. (C) 2008 Elsevier Inc. All rights reserved.