We present a hybrid Finite-Volume/Discontinuous-Galerkin (FV/DG) framework for the simulation of immiscible, compressible, multispecies flows on unstructured grids, with algebraic THINC reconstruction for the material interfaces. This procedure aims to reduce the interface smearing introduced by the adoption of diffuse-interface models and caused by numerical dissipation, by strategically employing a high-order DG discretisation in smooth flow regions, and activating a FV-type reconstruction within the cells containing discontinuous flow features, detected by a troubled-cell indicator. The efficient and robust compact WENOZ reconstruction is used to retain a high-order spatial discretisation and the implementation is performed in the UCNS3D open-source CFD solver [2]. The adoption of the THINC approach for the cells containing material interfaces has a double benefit in terms of maintaining sharp material interfaces and ensuring that the value of the volume fraction of each species is bounded within 0 and 1 throughout the simulation time. The computations are performed on unstructured meshes composed of arbitrary elements and using a five-equation model [3].