The immersed interface method is a quite general methodology for solving interface problems governed by differential equations. In this talk, I will first give an overview of this method. I will then present a boundary condition capturing immersed interface method, which can enforce the prescribed or free motions of rigid objects in a fluid wtih desirable numerical stability, accuracy and efficiency. Last, I will derive some principal jump conditions across a two-fluid interface, and present some thoughts on how to use them in the immersed interface method for simulation of two-fluid flows.