Fractured vuggy porous media continue to challenge the flow simulation research involving mass and/or heat transfer processes. Here, we report a coupled multiscale and multi-continuum approach developed to improve the modeling of multiphase flow through fractured vuggy porous media involving multi-continuum mass transfers. Multiple levels of fractures can be not only modeled as different superimposed continua but also embodied as discrete fracture networks based on their geometrical characteristics. Different configurations of vuggy existence can also be handled by a continuum and/or their discrete representations. We develop a systematic coupling using Multiscale Finite Element Method (MsFEM) as a framework for coarsening and refinement. MsFEM is used to capture subgrid scale heterogeneities and interactions through multiscale basis functions calculated based on the multi-continuum background. Unstructured mesh is applied to model discrete fractures in arbitrary directions and discrete vugs with complex geometries. This paper presents a significant advancement in terms of elevating the limitations of the multi-continuum models in handling complex fracture and/or vug geometry and extending the model reduction capability of MsFEM. Several numerical examples are carried out to demonstrate the capability of the proposed coupling method. (C) 2017 Elsevier Ltd. All rights reserved.