The present paper focuses on the simulation of compressible three-component flows interacting with surrounding deformable and immersed structures. For this purpose, a barotropic three-component model assuming instantaneous kinematic and mechanical equilibria is discussed. The mathematical properties of the system, the structure of the waves, the expression of the Riemann invariants and the existence of a mathematical entropy are thus examined. The link between the present model and the extension to three components of the Kapila model is discussed. An HLLC-type solver for the present three-component model based on the mathematical structure of the system is then described. The multi-fluid solver used is coupled with an updated Lagrangian approach used for the structural domain. Arbitrary Lagrangian-Eulerian (ALE) approach and Immersed Boundary Method (IBM) are here considered and compared for their capability to account for fluid-structure interactions (FSI). A series of Riemann problems with available analytical solutions are regarded to assess the used numerical approaches: Eulerian on fixed grids, ALE on moving grids and IBM with independent fluid and structure meshes. Finally, ALE and IBM methods are used to simulate an experimental configuration involving complex FSI problems with a multi-material flow and structural plastic deformations. The numerical results presented show a good agreement with the experimental data.