Modeling the interface progression between two immiscible fluids in a porous medium using the multi-scale homogenization method is a significant challenge with applications in engineering, such as prediction of air bubble formation in resin transfer molding (RTM). For accurate predic tions, it is required to distinguish between the mold scale and microscopic fiber scale, because air bubble formation depends on the non-uniform flow velocity across the different scales of the fibrous medium. While Darcy’s law is commonly used for flow in porous media, recent studies, such as those by Blanco et al [1]. and Shakoor and Park [2], have applied numerical homogenization schemes to model such flows by appling Navier-Stokes equations. In particular, Shakoor and Park implemented a strongly coupled multi-scale model. This study extends their approach to address two-phase flow problems, to increase the model capacity. For interface tracking in two-phase flows, volume of fluid and level-set methods have been commonly adopted. They are not yet integrated into a multi-scale framework. This study models the migration of air bubbles within fiber tows along the epoxy resin. We use the continuum surface force method to take into account the surface tension at the air-resin interface, all in a multi-scale framework based on homogenization. The Stokes model for each phase is solved using stable finite elements in the fine scale. Then, the resulting velocity is used to advect the interface and solved using the same numerical scheme. Macroscopic models for fluid and interface are derived using multi-scale virtual power principles. Finally, a strong coupling resolution between the two scales is implemented. Results show the multi-scale approach improves the computational efficiency, compared to single-scale methods, especially for the cases of small fiber diameters and large macroscopic domains.