Amphiphilic block copolyethers assemble into membranes with thickness between 2.4 and 7.5 nm. The vesicular morphology has been confirmed by small-angle X-ray scattering combined with electron microscopy for diblock copolymers and triblock copolymers of both architectures. The scaling of the membrane thicknesses with the length of the hydrophobic block is in good agreement with the strong segregation theory for block copolymer melts, indicating a mixed and stretched conformation of the hydrophobic chain inside the vesicle membrane. This result is in contrast to previously published results where the hydrophobic membranes were observed to have bilayer geometry and polymer chains that are relatively unperturbed from their ideal Gaussian dimensions.