Vesicles are widely used as model cells in biology and medicine and are also potentially useful as drug carriers and other industrial encapsulating devices. To facilitate the practical implementation of vesicles, as well as to gain a fundamental understanding of the process of vesicle formation, we have developed a molecular-thermodynamic theory to describe the formation of two-component mixed vesicles in aqueous solutions. The central quantity in this theory is the free energy of vesiculation, which is calculated by carefully modeling the various free-energy contributions to vesiculation. In particular, we (i) estimate the surfactant-tail packing free energy using a mean-field approach that accounts for the conformations of the surfactant tails in the vesicle hydrophobic region, (ii) adopt a more accurate equation of state in the calculation of the surfactant-head steric repulsions, and (iii) utilize the nonlinear Poisson-Boltzmann equation to calculate the electrostatic interactions in the case of mixed cationic/anionic charged vesicles. Particular attention has also been paid to issues such as the location of the outer and inner steric-repulsion surfaces in a vesicle and the curvature correction to the interfacial tensions at the outer and inner hydrocarbon/water vesicle interfaces. By knowing only the molecular structures of the surfactants involved in vesicle formation and the solution conditions, our theory can predict a wealth of vesicle properties, including vesicle size and composition distribution, surface potentials, surface charge densities, and compositions of vesicle leaflets. More importantly, this theory enables us to gain an understanding of (i) the underlying mechanisms of stabilization in mixed cationic/anionic vesicular systems, (ii) the effect of the interplay between the various intravesicular free-energy contributions on vesiculation, and (iii) the role of the distribution of surfactant molecules between the two vesicle leaflets in vesicle formation. As an illustration, the theory has been applied to describe vesicle formation in an aqueous mixture of cetyltrimethylammonium bromide (CTAB) and sodium octyl sulfate (SOS). In this system, the vesicles are found to be stabilized entropically, with a predicted mean radius of about 1200 Angstrom for a mixture containing 2 wt% surfactant and a CTAB/SOS weight ratio of 3/7, a value which compares well with the experimentally measured value of 1300 Angstrom. In addition, the predicted outer surface potential of -72 mV is consistent with the measured zeta potential value. The effect of added salt on vesicle properties has also been studied using this theory, and the predicted results conform well to experimental observations.