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.