In this work, a robust computational method with the four-equation model is proposed to simulate compressible multi-phase multi-component flows. An ENO-type numerical scheme is designed to be consistent with the thermodynamic equilibrium assumptions of the four-equation multi-phase model, discretely enforcing the interface equilibrium condition — preventing numerical oscillations in pressure, velocity, and temperature around isothermal material interfaces. Critically, the proposed numerical method for the four-equation model accomplishes this without requiring explicit equations for volume fraction or other redundant transport equations for variables including mixture equation of state parameters, as is commonly done for the five-equation model. Additionally, consistent mixing rules are used to derive a non-dilute species diffusion model and thereby extend the conservative diffuse interface (CDI) model to multi-component systems. Together, these models prevent unphysical numerical leakage of species across phase interfaces. The presented test cases show that this consistent numerical method is equally applicable for regimes ranging from single-phase to multi-phase multi-component flows without retuning numerical parameters. When augmented with an existing positivity-preserving limiter for handling compressible multiphase flows, we show that the proposed computational method can robustly handle extreme conditions including strong shock-interface interactions, within the four-equation modeling framework. The proposed models and numerical schemes are implemented in the highly parallel Hypersonic Task based Research (HTR) Solver, and high-resolution simulations are performed using both CPUs and GPUs.