Polymer electrolyte membranes (PEMs) selectively transport ions and polar molecules in a robust yet formable solid support. Tailored PEMs allow for devices such as solid-state batteries, `artificial muscle' actuators and reverse-osmosis water purifiers. Understanding how PEM structure and morphology relate to mobile species transport presents a challenge for designing next-generation materials. Material length scales from subnanometre(1,2) to 1 mu m (refs 3,4) influence bulk properties such as ion conductivity and water transport. Here we employ multi-axis pulsed-field-gradient NMR (ref. 5) to measure diffusion anisotropy, and (2)HNMRspectroscopy(5,6) and synchrotron small-angle X-ray scattering(7) to probe orientational order as a function of water content and of membrane stretching. Strikingly, transport anisotropy linearly depends on the degree of alignment, signifying that membrane stretching affects neither the nanometre-scale channel dimensions nor the defect structure, causing only domain reorientation. The observed reorientation of anisotropic domains without perturbation of the inherent nematic-like domain character parallels the behaviour of nematic elastomers(8), promises tailored membrane conduction and potentially allows understanding of tunable shape-memory effects in PEM materials(9). This quantitative understanding will drive PEM design efforts towards optimal membrane transport, thus enabling more efficient polymeric batteries, fuel cells, mechanical actuators and water purification.