The bilayer membrane permeability of block copolymer vesicles ("polymersomes") with ionic liquid interiors dispersed in water is quantified using fluorescence quenching. Poly((1,2-butadiene)-b-ethylene oxide) (PB-PEO) block copolymer vesicles in water with their interiors filled with a common hydrophobic ionic liquid, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide, were prepared containing a hydrophobic dye, Nile Red, by intact migration of dye-encapsulated vesicles from the ionic liquid to water at room temperature. A small quencher molecule, dichloroacetamide, was added to the aqueous solution of the dye-loaded vesicles, and the permeation of the quencher passing through the membrane into the interior was determined from the fluorescence quenching kinetics. Rapid permeation of the quencher across the nanoscale membrane was observed, consistent with the high fluidity of the liquid polybutadiene membrane. Two different PB-PEO copolymers were employed, in order to vary the thickness of the solvophobic membrane. A significant increase in membrane permeability was also observed with decreasing membrane thickness, which is tentatively attributable to differences in quencher solubility in the membranes. Quantitative migration of the vesicles from the aqueous phase back to an ionic liquid phase was achieved upon heating. These microscopically heterogeneous and thermoresponsive vesicles with permeable and robust membranes have potential as recyclable nanoreactors, in which the high viscosity and capital expense of an ionic liquid reaction medium can be mitigated, while retaining the desirable features of ionic liquids as reaction media, and facile catalyst recovery.