Subsurface hydrogen (H2) storage has emerged as a promising solution for overcoming challenges in renewable energy generation. The feasibility of geologic hydrogen storage in saline aquifers requires a comprehensive analysis of multiphase fluid flow within reservoir formations. This study investigates the water-hydrogen transport properties of homogeneous quartz-arenite Berea sandstone and heterogeneous Ironton/Galesville containing clay-rich bedding planes. An experimental setup is introduced to measure the intrinsic and water-hydrogen relative permeability under representative in-situ stress conditions. Single-phase flow tests reveal the bedding-normal intrinsic permeability of Ironton/Galesville to be ⁓10−17 m2 – three to four orders of magnitude lower than the one measured for bedding-parallel orientation and Berea sandstone. In the two-phase flow tests, hydrogen exhibits significantly lower relative permeability than water primarily due to its lower viscosity. Hysteresis in relative permeability is observed only in primary episode, disappearing for the consecutive drainage and imbibition cycles. The strongest hysteresis is identified in vertical Ironton/Galesville, attributed to pore structure complexity and variation in capillary responses. Comparison with relative permeability estimation based on pore structure analysis underscores the limitation of such methods and highlights the importance of direct measurements. These findings provide critical insights into water-hydrogen flow mechanisms and offer valuable data for evaluating subsurface hydrogen potential.