Metallic interfaces are locations where hydrogen (H) is expected to segregate and lead to the formation and stabilization of defects. This work focuses on the tungsten/copper (W/Cu) interface built according to the W bcc (001)/Cu hcp (11-20) orientation. H behavior is subsequently determined at the interface and in its vicinity with electronic structure calculations based on the density functional theory (DFT). The electronic and vibrational properties determined in this way followed a thermodynamic treatment to deliver the solubility of H as a function of the temperature and chemical potential. The 96 interstitial positions we investigated reveal that H predominantly occupies the octahedral (Oh) sites in the copper network. Reversely, H exclusively occupies the tetrahedral (Td) sites in the tungsten network. The solubility of H is higher in the interface plane where both octahedral and tetrahedral sites are occupied. Despite this work is a first step toward kinetic modeling of hydrogen transport across the W/Cu interface, we conclude that the W bcc (001)/Cu hcp (11-20) would behave like a sink where hydrogen isotopes could accumulate.