In this paper, we introduce a compressible formulation for dealing with 2D/3D compressible interfacial flows. It integrates a monolithic solver to achieve robust velocity–pressure coupling, ensuring precision and stability across diverse fluid flow conditions, including incompressible and compressible single-phase and two-phase flows. Validation of the model is conducted through various test scenarios, including Sod’s shock tube problem, isothermal viscous two-phase flows without capillary effects, and the impact of drops on viscous liquid films. The results highlight the ability of the scheme to handle compressible flow situations with capillary effects, which are important in computational fluid dynamics (CFD).