A process for making monodisperse liposomes having lipid bilayer membranes involves fewer, simpler process steps than do related prior methods. First, a microfluidic, cross-junction droplet generator is used to produce vesicles comprising aqueous-solution droplets contained in single-layer lipid membranes. The vesicles are collected in a lipid-solvent mix that is at most partially soluble in water and is less dense than is water. A layer of water is dispensed on top of the solvent. By virtue of the difference in densities, the water sinks to the bottom and the solvent floats to the top. The vesicles, which have almost the same density as that of water, become exchanged into the water instead of floating to the top. As there are excess lipids in the solvent solution, in order for the vesicles to remain in the water, the addition of a second lipid layer to each vesicle is energetically favored.