The structure of the lamellar phase of the ternary system of palmitoyloleoylphosphatidylcholine (POPC)/tetra(ethylene oxide) monododecyl ether (C12E4) has been characterized in detail by a X-ray and neutron scattering and by H-2 NMR spectroscopy. The addition of small amounts of surfactant to the POPC bilayers causes the bilayer to become more rigid, while the addition of large amounts of surfactants induces a fluidization of the structure. Here, we report a Monte Carlo study of the underlying mechanisms yielding these changes in the orientational order of POPC/C12E4 bilayers. The study employs a lattice Monte Carlo dynamics algorithm that rests on the assumption that the conformational dynamics of chain molecules can be described as the superposition of local structural rearrangements involving short-chain segments. This approach is particularly useful for following structural and conformational changes on time scales longer than those associated with the gauche/trans isomerization of hydrocarbon chains. The simulations reproduce the principal features of the order parameter profiles of the surfactant molecules found in pure bilayers and bilayers of POPC/C12E4 mixtures and provide a physical framework for understanding the experimental observations.