Compressible multiphase flows are at the heart of a great number of engineering applications in several domains. Some examples include the aerospace industry, since many rocket propulsion systems rely on the injection of a liquid reactant into the combustion chamber and the efficiency of the combustion is directly related to the atomization process. Other applications include the civil nuclear industry safety analysis but also the naval industry for which underwater solid propulsion systems are of great interest. The design and optimization requirements of these systems lead to an increasing need for predictive numerical simulations. Diffuse interface models are widely used for these tasks as they provide a good trade-off between accuracy and robustness. We consider the class of Baer-Nunziato type of models, in which the most general one allows for full disequilibrium between the two-phases. Reduced order models are obtained by assuming some local equilibrium (velocity, pressure, temperature or chemical potential equilibrium). Among this hierarchy of models, the pressure and velocity equilibrium model of Kapila et al is of particular interest. It allows to recover the classical Wood sound velocity for two-phase mixtures while still allowing thermal disequilibrium which is paramount for many applications such as high-temperature jets impinging on liquid surfaces and for proper modelling of phase changes. Several strategies to solve this model rely on a 6-equation model endowed with stiff pressure relaxation terms. For cavitating flows, an accurate computation of the pressure equilibrium is particularly important to compute the mass transfer fluxes. The purpose of the present contribution is to study the assumptions on the thermodynamics of the two phases and its impact on the mathematical structure of the resulting system of PDEs (where potentially several relaxation processes are involved either relying on finite-rate or instantaneous relaxation source terms). We propose an analysis of the pressure relaxation process in terms of thermodynamically admissible paths and propose a robust numerical scheme, which preserves the set of admissible states of the system. The robustness and accuracy of the proposed numerical scheme involving convection and sources is then assessed on several challenging configurations including shock-interface interactions and cavitating flows, such as shock-droplet interaction or Richtmyer–Meshkov instability.