This paper studies an Eulerian diffuse interface model for the simulation of compressible multifluid and two-phase flow problems. We first show how to derive this model from a seven equation, two pressure, two velocity model of Baer-Nunziato type using an asymptotic analysis in the limit of zero relaxation time. We then study the mathematical properties of the system, the structure of the waves, the expression of the Riemann's invariants and the existence of a mathematical entropy. We also describe two different numerical approximation schemes for this system. The first one relies on a linearized Riemann solver while the second uses more heavily the mathematical structure of the system and relies on a linearization of the characteristic relations. Finally, we present some numerical experiments and comparisons with the results obtained by the two pressure, two velocity model as well as some test cases and comparisons with another five equation model recently proposed for interface computations between compressible fluids.