The present work is devoted to the study of a system of conservation laws which arises when modelling compressible bifluid flows, in view of preliminary inertial confinement fusion simulations. By opposition to usual multiphase models, the present system of PDE’s turns out to be in fully conservative form, what is of great practical interest in the development of usual numerical approaches and for the capture of shocks. The study is strongly conditioned by the so-called isobar-isothermal closure. We propose a numerical scheme for the approximate resolution of the model which respects positivity of mass fractions. Numerical results illustrate the interest of the model and the method on classical bifluid test-cases.