the shape transformations and composition variation of two-component model lipid membrane isolated vesicles are studied. these are studied as aggregates in low concentration solutions so that the vesicles are isolated from each other and interaction effects can be ignored. the seminal work of julicher and lipowsky derived a curvaturefunctional free energy, which has predicted or verified many of the experimentally observed behaviors of model vesicles. one aspect that has not been well explored is the composition variation of the liquid domains. in this work, the theory of julicher and lipowsky is modified to include couplings between the curvature and composition but the shape of the vesicle is restricted to include only ellipsoids of varying degree of eccentricity and constant area. we also introduce a free energy to describe bilayered micelles (“bicelles”). the energetics of this structure is studied and phase diagrams are found for various vesicle-bicelle transitions. the properties of liquid domains, including compositional variations with temperature are also discussed. these results are then compared to experiments on vesicles and bicelles using small angle neutron scattering and nuclear magnetic resonance.