Multi-phase polymer melt processing techniques, e.g., multi-layer co-extrusion and multi-melt multi-injection molding (M3IM), are typical methods for preparing multilayer composites. Numerical simulations are now broadly acknowledged to be an advanced and effective method to investigate the evolution of the interface between the melts during these processing techniques. However, how to describe the sharp interface between the melts precisely is still a big challenge. Herein, five different interpolation schemes were used to investigate the melt penetration in M3IM, paying close attention to the effects of different schemes on interface diffusion, wrinkle, and shape. In addition, the morphologies of the interface were characterized experimentally. By comparing the numerical results and experimental results, it can be concluded that the compressive interface capturing scheme for arbitrary meshes (CICSAM) is the most accurate method. Our work is instructive for expounding the variation patterns of interfacial morphologies during the multi-phase polymer melt processing.