Recent experiments have demonstrated transport and separation of hydrogen isotopes through the van der Waals gap in hexagonal boron nitride and molybdenum disulfide bulk layered materials. However, the experiments cannot distinguish if the transported particles are protons (H⁺) or protium (H) atoms. Here, reported are the theoretical studies, which indicate that protium atoms, rather than protons, are transported through the gap. First-principles calculations combined with well-tempered metadynamics simulations at finite temperature reveal that for h-BN and MoS₂, the diffusion mechanism of both protons and protium (H) atoms involves a hopping process between adjacent layers. This process is assisted by low-energy phonon shear modes. The extracted diffusion coefficient of protium matches the experiment, while for protons it is several orders of magnitude smaller. This indicates that protium atoms are responsible for the experimental observations. These results allow for a comprehensive interpretation of experimental results on the transport of hydrogen isotopes through van der Waals gaps and can help identify other materials for hydrogen isotope separation applications.