Liquid-crystalline cubic-phase nanoparticles (CPNPs) (known as Cubosome particles), based on the lipid glycerol monooleate and stabilized by the nonionic block copolymer Pluronic F-127, interact with supported model membranes consisting of dioleoylphosphatidylcholine (DOPC) in a complex and dynamic fashion. Neutron reflectivity measurements on the interaction of CPNPs with bilayers of different coverage have increased our understanding of an interfacial exchange mechanism that is relevant to delivery applications. To access the composition of the adsorption layer, the method of isotopic contrast between the components was exploited by using DOPC with perdeuterated acyl chains, which are distinguishable (high scattering contrast) from the hydrogenous components of the CPNPs. The exchange of material between CPNPs and the bilayer takes place regardless of the initial bilayer coverage. However, this parameter has a strong influence on the physical nature of the layer formed upon interaction. For a bilayer of "high coverage" (80%), extensive exchange takes place between the CPNP components and the bilayer, and at steady state the surface layer comprises 72% glycerol monooleate and 8% DOPC, with no change in the solvent content. An analogous experiment involving pure glycerol monooleate liquid crystals shows that lipid exchange occurs even in the absence of the stabilizing polymer. For bilayers of "low coverage" (55%), the exchange mechanism involves an initial adsorption of material from the CPNPs to fill in the bilayer defects. However, most of the bilayer breaks up and only 15% coverage remains after 30 h. The evolution of a Bragg diffraction peak was monitored in this case to show that the bound nanoparticles occupy >7% surface coverage and have a periodicity in the density of the internal lipid structure that decreases with time. This progression is attributed to the incorporation of d-DOPC molecules within the internal cubic structure of the nanoparticles. The broadening of the diffraction peak with time, together with a final mean position that is closely related to the periodicity of the lamellar phase organization of GMO, shows that the lipid-exchange process results in either a contraction of the unit cell of the cubic-phase nanoparticles or a progression of the lipid arrangement to the lamellar phase.