Membrane technologies with low environmental impacts and ease of use have a wide spectrum of applications, with the potential to provide more sustainable solutions in domains such as water, energy and pollution treatment. However, the design of membranes is subject to a trade-off between ion conductivity and selectivity. Here we show a composite polymeric membrane that breaks this dilemma and supports both high proton conductivity (80.1 mS cm−1) and good vanadium ion selectivity (2.01 × 105 S min cm−3). Underlying this synthetic success is a flow-processing technique through which zeolite nanosheet fillers are oriented in a preferred direction throughout a polymer Nafion matrix. As a result, pairing this aligned membrane with a vanadium flow battery leads to a high energy efficiency of >80% at 200 mA cm−2 and remarkable stability over 1,000 cycles. This work enables the design of membranes that combine otherwise mutually exclusively properties for many possible applications beyond energy storage.