The work shows the influence of interface conditions between materials (perfectly joined) on H diffusion and retention. Implementation in the FESTIM code of the continuity of chemical potential across interfaces is detailed, analytically verified and comparisons and cross-check with TMAP and Abaqus codes are performed. W/Cu and Cu/Eurofer interfaces were simulated in 1D. Jumps of solute concentration at this interface impact the outgassing flux. Comparisons were performed assuming a concentration continuity instead of chemical potential continuity and show ten % of under or over estimation between both cases, depending of the values of solubility. 2D simulations of ITER monoblocks show low impact of the interface condition on the inventory. Effect of non-equilibrium interface on permeation and non perfect junction such as trap generation could be explored in future work.