We present an immersed interface method (IIM) for solving the 2D compressible viscous Navier-Stokes equations in the supersonic limit. We employ an IIM based on the ghost-point technique combined with a shock-detection method in order to handle discontinuities in the flow variables. The shock-detection step allows us to use a slower, more dissipative method near the shocks, while a faster, non-dissipative method is used away from the shock discontinuities. We present the results for a supersonic flow around a cylinder.