Self-assembled membranes of amphiphilic diblock copolymers enable comparisons of cohesiveness with lipid membranes over the range of hydrophobic thicknesses d = 3-15 nm. At zero mechanical tension the breakdown potential Vc for polymersomes with d = 15 nm is 9 V, compared to 1 V for liposomes with d = 3 nm. Nonetheless, electromechanical stresses at breakdown universally exhibit a V2 c dependence, and membrane capacitance shows the expected strong d dependence, conforming to simple thermodynamic models. The viscous nature of the diblock membranes is apparent in the protracted postporation dynamics.