Understanding the process of moisture sorption and desorption in multi-material system is important for a variety of applications, such as electronic packaging, food packaging, hygrothermal building performance, and material aging and compatibility. In this work we model the sorption-desorption process in multi-material system by coupling diffusion with equilibrium Henry's absorption and kinetic Langmuir adsorption. A finite volume method with implicit Euler time-stepping scheme was applied to solve the coupled unsteady diffusion-sorption equations. The code was validated against existing experimental data for moisture uptake and outgassing in polymeric materials. The proposed numerical method is shown to be well adapted for predicting interfacial mass transfer during sorption-desorption in multi-material system.