We introduce a new method to efficiently track complex interfaces among multi-phase immiscible fluids. Unlike existing techniques, we use a mesh-based representation for global liquid surfaces while selectively modeling some local surficial regions with regional level sets (RLS) to handle complex geometries that are difficult to resolve with explicit topology operations. Such a semi-explicit surface mechanism can preserve volume, fine features and foam-like thin films under a relatively low computational expenditure. Our method processes the surface evolution by sampling the fluid domain onto a spectrally refined grid (SRG) and performs efficient grid scanning, generalized interpolations and topology operations on the basis of this grid structure. For the RLS surface part, we propose an accurate advection scheme targeted at SRG. For the explicit mesh part, we develop a fast grid-scanning technique to voxelize the meshes and introduce novel strategies to detect grid cells that contain inconsistent mesh components. A robust algorithm is proposed to construct consistent local meshes to resolve mesh penetrations, and handle the coupling between explicit mesh and RLS surficial regions. We also provide further improvement on handling complicated topological variations, and strategies for remeshing mesh/RLS interconversions.