  We present an isoparametric unfitted finite element approach of the CutFEM or
Nitsche-XFEM family for the simulation of two-phase Stokes problems with slip
between phases. For the unfitted generalized Taylor--Hood finite element pair
$\mathbf{P}_{k+1}-P_k$, $k\ge1$, we show an inf-sup stability property with a
stability constant that is independent of the viscosity ratio, slip
coefficient, position of the interface with respect to the background mesh and,
of course, mesh size. In addition, we prove stability and optimal error
estimates that follow from this inf-sup property. We provide numerical results
in two and three dimensions to corroborate the theoretical findings and
demonstrate the robustness of our approach with respect to the contrast in
viscosity, slip coefficient value, and position of the interface relative to
the fixed computational mesh.
