Compressible or weakly compressible liquid-gas flows occur in many fields such as liquid fuel injection, plunging waves, cavitation, sloshing, drowning damaged nuclear reactor, phase change heat transfer, pipeline of two-phase flows, etc. Most numerical simulations dedicated to the aforementioned applications use an incompressible formalism, which does not take into account the compressibility effects and density variation among each phase. However, compressibility can have a significant effect in a wide range of configuration, from liquid jet injection (cavitation inside an injector) to breaking wave configuration (impact of the entrained air or bubbles). This work aims at providing numerical tools, allowing simulations of two-phase flows covering a large range of Mach number, incorporating surface tension, acoustic/compressible effects, large density ratio, proper jump conditions, viscous effects, at High Reynolds and High Weber number. We propose achieving this challenging task by improving the two-phase flows aspect of the pressure-based method proposed by Huber et al (2015) [Journal of Computational Physics, Volume 302, 2015, Pages 439-468] by combining it with an accurate and conservative interface representation : the Coupled Level Set/VOF interface capturing method. First, a one-dimensional oscillating water column configuration is investigated to perform the validation of this method. Then, a three-dimensional two-phase HIT configuration is studied to demonstrate the behavior and the potential of this method in presence of breakup, coalescence and vaporization processes.