We consider the phase behavior of an aqueous solution of a mixture of two amphiphiles having different structural properties: a phospholipid, which tends to self-assemble into extended flat bilayers forming closed vesicles, and a surfactant, which self-organizes into small, strongly curved micelles. In a mixture of the two amphiphiles, the two kinds of aggregates, mixed vesicles, and the mixed threadlike micelles can be formed in coexistence with aqueous solution of surfactant monomers. The composition-induced transition between the micelles and the vesicles is generally assumed(1) to be determined solely by the surfactant-to-lipid ratio within the aggregates and to be independent of the aqueous concentrations of the amphiphiles per se. While this approach described successfully the experimental phase boundaries in the range of relatively high lipid concentrations L, it demonstrated an internal contradiction upon extrapolation to low L. The goal of the present study is to develop a model free of this self-inconsistency. For that we consider the effects of the finite size of the threadlike micelles on the phase behavior of the system. Specifically, we treat the vesicular phase and the aqueous solution of the surfactant monomers using the previous approach but present a different thermodynamic description of the micelles as built of cylindrical parts and inhomogeneous end-caps, analogous to Gibbs treatment of interfaces. Based on this description, and accounting for the translational entropy of the micelles, we determine the chemical potentials of the lipid and surfactant in the micellar phase. Equalizing the chemical potentials of each amphiphilic compound in all phases available for it, we find the conditions of coexistence of different phases and, by so doing, determine the phase diagram. We show that the proposed approach describes self-consistently the existing experimental data. Furthermore, we use our analysis to make several testable predictions and perform the experiments, which verify these predictions and support the conclusions of the study.