Designing tailored block copolymers represents a viable strategy for building polymer membranes with fruitful combinations of properties, such its the high ionic or small molecule conductivity and high mechanical strength needed for applications such as fuel cells and reverse-osmosis water purification. Here we present a systematic study of water transport and morphological alignment in a class of poly(arylene ether sulfone) hydrophilic-hydrophobic multiblock copolymer membranes and compare these with Nafion 212. Multiaxis pulsed-field-gradient NMR yields diffusion anisotropy, the ratio of diffusion coefficients measured both in plane (D-parallel to) and through plane (D-perpendicular to), as a function of water uptake and block lengths. As block mass increases, diffusion anisotropy exhibits an increasing dependence on water uptake, in contrast to Nafion 212, where diffusion is isotropic and displays no dependence on water uptake. H-2 NMR spectroscopy oil absorbed D2O further probes membrane alignment modes. Both types of measurements corroborate uniformly ordered planar structures oriented through the membrane plane in accordance with a lamellar morphology previously observed locally with microscopy. The combination of these two measurements also provides insights into average defect distributions.