This study presents a method to perform direct numerical simulation (DNS), in the sense of turbulence, of two-phase flows with interfaces. It is based on the compressible diffuse interface model introduced by the second gradient theory. This model assumes a continuous variation of the thermodynamic variables in the interface and add to their description a dependency on the density gradient. The interface widths as predicted by the model fall way below the typical relevant turbulent scales. We propose here a thermodynamically consistent method to thicken the interface in order to perform calculations on typical DNS meshes. The modified model has been integrated and validated on canonical configurations. It has then been applied to more complex cases such as colliding three-dimensional droplets and the breakup of two-dimensional liquid jets.