Microcapsules with liquid cores and solid shells are attractive as dispersible protective micron-sized containers. Applications that rely on molecular mass transport often require a combination of size selectivity, high permeability, and mechanical stability. Capsule architectures that combine all these features represent a material property, design, and fabrication challenge. In this work, the design of an asymmetric microcapsule shell architecture is reported to achieve a good combination of the desired features. Poly(methyl methacrylate) phase-inverted microcapsules featuring an asymmetric graded macroporous shell covered with a dense skin separation layer are obtained from water-in-oil-in-water double emulsion drops that are phase-inverted in a water-based coagulation bath. The phase-inverted microcapsules exhibit good mechanical stability and allow for high permeability of its shell membrane with molecular size dependence.