Fluid-fluid and fluid-solid coupling in multiphase 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 [1] provided an elegant approach to represent integration of Heaviside and Direct distributions exactly for common cell types cut by moving interfaces. In [2] that approach was used to implement and extend at CutFEM method developed for the Oseen problem [3] 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. For the jump conditions between the fluids, the method [4] 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 the complete three-phase method and application to granular media.