Polymersomes, vesicles composed of bilayer membranes of amphiphilic block-copolymers, are promising delivery vehicles for long-term storage and controlled release of bioactives; enhanced stability of the membrane makes polymersomes potentially useful in a wide range of biological delivery applications by comparison with liposomes. However, unilamellar structure is intrinsically fragile when subjected to external stress. Here, we report a microfluidic approach to produce polymersomes with double bilayers, providing higher stability and lower permeability than unilamellar polymersomes. To achieve this, we developed a new design of a capillary microfluidic device to produce quadruple-emulsion drops which serve as a template for the polymersomes-in-polymersomes. When two bilayers are attracted by depletion in polymersomes-in-polymersomes, the inner polymersomes protrude and bud, forming double bilayers. We confirm these structures are indeed double bilayers using microaspiration and selective doping of the leaflets with nanoparticles. The resultant polymersomes have great potential as highly stable and biocompatible microcarriers for robust encapsulation and storage of bioactives such as drugs, cosmetics and nutrients.