This paper explores fluid-structure interaction (FSI) of two-phase flows involving a three-phase contact line using the extended Discontinuous Galerkin (XDG) method within the Euler-Euler framework. The fluid dynamics are governed by the incompressible Navier-Stokes equations, while the soft solid mechanics of the Kelvin-Voigt material are described using the Navier-Cauchy equations. Coupling conditions between the fluid and solid phases are established through continuity of velocity and stress at the interface, mirroring the conditions applied at the boundary between two fluid phases. At the three-phase contact line, the generalized Young’s equation is employed to maintain consistency. The spatial discretization of the governing equations is also introduced. A convergence study of FSI is presented, validated against an analytical solution, alongside several classical FSI test cases. Additionally, the paper showcases 2D and 3D simulations of a droplet interacting with a soft substrate at a three-phase contact line, highlighting the method’s capabilities and practical implications.