Fluid-fluid and fluid-solid coupling in multi-phase flows have distinctly different requirements for numerical discretization methods that make implementation of effective methods for air-water-solid models difficult to achieve. One source of these difficulties arises from the different physics at fluid-solid interfaces and fluid-fluid interfaces. Another is the difficulty of robustly and accurately integrating along these moving interfaces. The equivalent polynomials technique provided an elegant approach to represent integration of Heaviside and Direct distributions exactly for common cell types cut by moving interfaces. This approach was used to implement and extend the CutFEM method developed for the Oseen problem to incompressible fluid-solid interaction problems where the CutFEM method is convenient for enforcing the fluid-solid jump conditions for rigid solids with a stabilized Nitsche method. In this work we extend the approach to include a second incompressible fluid using immersed interface approach. For the jump conditions between the fluids, the method is convenient as it allows representation of discontinuous viscosity, density, and pressure across the interface without introduction of extra degrees of freedom or ghost penalties that would be required by a Nitsche method. We present details of a three-phase coupled model with immersed FEM method for fluid-fluid interaction and cutFEM for fluid-solid interaction and application to granular media.