Hydrogen's contribution to a sustainable energy transformation requires intermittent storage technologies, e.g., underground hydrogen storage (UHS). Toward designing UHS sites, atomistic molecular dynamics (MD) simulations are used here to quantify thermodynamic and transport properties for confined aqueous H2. Slit-shaped pores of width 10 and 20 Å are carved out of kaolinite. Within these pores, water yields pronounced hydration layers. Molecular H2 distributes along these hydration layers, yielding solubilities up to ∼25 times those in the bulk. Hydrogen accumulates near the siloxane surface, where water density fluctuates significantly. On the contrary, a dense hydration layer forms on the gibbsite surface, which is, for the most part, depleted of H2. Although confinement reduces water mobility, the diffusion of aqueous H2 increases as the kaolinite pore width decreases, also a consequence of water density fluctuations. These results relate to H2 permeability in underground hydrogen storage sites.