Energy Storage and conversion devices require an ion-exchange membrane to accomplish high transmission of charge-balancing ions and separation of anode and cathode electrolytes/gases from mixing. These critical functions of membranes play a pivotal role in ensuring device optimum performance and higher efficiency. Most conventional membranes suffer huge ionic and molecular species cross-permeation resulting in low energy efficiency and material degradation. In this work, hydrogen permeability and proton transmission through membrane electrode assemblies (MEAs) that contain a monolayer of hexagonal boron nitride, single-layer and bi-layer graphene were investigated in a gas-phase small-scale cell and a liquid cell. We found that the hydrogen crossover flux through MEAs with 2D materials was inhibited by at least a factor of 5 as compared to the one without. Single-layer graphene and boron nitride enabled high proton transmission, but bi-layer graphene inhibited proton conduction. Defect visualization of 2D materials by chemical treatment with a low ferric chloride concentration followed by imaging using a digital microscope revealed few atomic-scale defects in graphene. These findings suggest that a monolayer of 2D material may provide good selectivity for energy conversion and storage devices by blocking species crossover while allowing high proton transmission.