Massively cross-linked and property-tunable membranes have been fabricated by free radical polymerization of self-assembled, block copolymer vesicles − polymersomes. Similar efforts with cross-linkable lipids would appear frustrated in the past due to at least two factors:  limited reactivity and membrane fragility under local stresses of nano-confined cross-linking. We describe here a diblock copolymer of poly(ethylene oxide)-polybutadiene that has a hydrophilic weight fraction like that of lipids and forms robust fluid phase membranes in water. The polymersomes sustain free radical polymerization of the hydrophobic butadiene, thereby generating a semipermeable nano-shell. Cross-linked giant vesicles prove stable in chloroform and can also be dehydrated and re-hydrated without rendering the ∼9 nm thick membrane core; the results imply defect-free membranes many microns-squared in area. Surface elastic moduli as well as sustainable wall stresses up to 10³ Atm, orders of magnitude greater than any natural lipid membrane, appear consistent with strong tethering between close-packed neighbors. The enormous stability of the giant vesicles can be tuned down for application:  blending in the hydrogenated analogue poly(ethylene oxide)-polyethylethylene modulates the effective elastic constants as well as the rupture strength by orders of magnitude. The results appear consistent with rigidity percolation through a finite-layer stack of two-dimensional lattices. Moreover, below the percolation limit, a regime of hyper-instability emerges, reflecting perhaps nanoscale demixing and suggestive of the limitations encountered with low reactivity lipids. The results provide general insights into covalent cross-linking within self-assembled nanostructures.