We introduce a novel framework for tracking multiphase interfaces with explicit contouring technique. In our framework, an unsigned distance function and an additional indicator function are used to represent the multiphase system. Our method maintains the explicit polygonal meshes that define the multiphase interfaces. At each step, distance function and indicator function are updated via semi- Lagrangian path tracing from the meshes of the last step. Interface surfaces are then reconstructed by polygonization procedures with precomputed stencils and further smoothed with a featurepreserving non-manifold smoothing algorithm to stay in good quality. Our method is easy to be implemented and incorporated into multiphase simulation, such as immiscible fluids, crystal grain growth and geometric flows. We demonstrate our method with several level set tests, including advection, propagation, etc., and couple it to some existing fluid simulators. The results show that our approach is stable, flexible, and effective for tracking multiphase interfaces.