In this study, a stable and robust interface-capturing method is developed to resolve inviscid, compressible two-fluid flows with general equation of state (EOS). The governing equations consist of mass conservation equation for each fluid, momentum and energy equations for mixture and an advection equation for volume fraction of one fluid component. Assumption of pressure equilibrium across an interface is used to close the model system. MUSCL-Hancock scheme is extended to construct input states for Riemann problems, whose solutions are calculated using generalized HLLC approximate Riemann solver. Adaptive mesh refinement (AMR) capability is built into hydrodynamic code. The resulting method has some advantages. First, it is very stable and robust, as the advection equation is handled properly. Second, general equation of state can model more materials than simple EOSs such as ideal and stiffened gas EOSs for example. In addition, AMR enables us to properly resolve flow features at disparate scales. Finally, this method is quite simple, time-efficient and easy to implement.