The immersed boundary (IB) method is a general numerical method for simulating fluid-structure interaction. In the past, the IB method was limited to uniform viscosities unless additional techniques were used to keep track of the interfaces between fluid regions. The present method overcomes this difficulty by embedding marker particles in the fluid that “spread” variations in viscosity and density onto the grid and are passively advected. We treat the non-uniform parts explicitly so that FFTs can be used, as in the constant coefficient case, but with an adjusted effective forcing term. Empirical convergence rates, which show second-order convergence for sufficiently smooth problems, will be presented. Red blood cells and heterogeneous flows through pipes are among possible applications of this method. Our preliminary simulations will be discussed.