Two-dimensional multiphase flows with material interface due to density difference are numerically simulated on an unstructured grid system by a Navier-Stokes solver developed by Myong and Kim (2006), since numerical computation for these flows is still known to be difficult, especially if the interface separates fluids of large different densities. This solver employs an unstructured cell-centered method based on a conservative pressure-based finite volume method, since the unstructured grid approach makes the solver very flexible in dealing with complex boundaries, and adopts a high resolution method (CICSAM) in a volume of fluid (VOF) scheme for the accurate phase interface capturing. The test cases are the Rayleigh-Taylor instability (density ratio of 2), the oil bubble rising in a partially filled container (density ratio of 2), the air bubble rising in a fully filled container with bubble shedding (density ratio of 100) and the droplet splash (density ratio of about 1000), which are typical benchmark problems among multiphase flows with material interface due to density difference. The present results are compared with other numerical solutions found in the literature. The present method (solver) efficiently and accurately simulates complex interface flows such as multiphase flows with material interface due to both density difference and instability.