Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressurevelocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics. Thus, this work presents a novel approach that combines the Godunov-type scheme for high-speed flows with the projection solution procedure for incompressible flows to address this challenge. To simulate compressible multi-component flows, this study employs the homogeneous model and solves its conservative form by the finite-volume method, which enables the application of the one-fluid model solution procedure while satisfying conservation. The proposed hybrid approach begins by splitting the inviscid flux into the advection part and the pressure part. The solution variables are first updated to their intermediate states by solving the advection part with the all-speed AUSM (Advection Upwind Splitting Method) Riemann solver. The advection flux in AUSM is modified to eliminate the pressure flux term that deteriorates the accuracy at the low Mach region. To prevent the advection flux from causing spurious velocities when surface tension is present, the pressure-velocity coupling term is modified to ensure it vanishes at material interfaces. Then, we derive the pressure Helmholtz equation to solve the final pressure and update the intermediate states to the solution variables at the next time step. The proposed hybrid approach retains the upwind property of the AUSM scheme for high Mach numbers while recovering central schemes and the standard projection solution for low Mach limits. We also prove that the proposed hybrid method is capable of solving the stationary contact discontinuity exactly. To accurately resolve the complex flow structures including shock waves and material interfaces without numerical oscillations, a newly proposed homogenous ROUND (Reconstruction Operator on Unified Normalised-variable Diagram) reconstruction strategy is employed in this work. By simulating high-speed compressible multiphase flows and incompressible multiphase flows, this study demonstrates the ability of the proposed method to accurately handle flow regimes across all Mach numbers. Its capability to address multi-physical processes at all Mach numbers is further validated through simulations of nucleate boiling and the Richtmyer-Meshkov instability with cavitation.