The Two-Fluid Model, an averaged model widely used in the modeling of two-phase compressible flows, generally fails to be hyperbolic in its basic formulation. However, interfacial forces such as the interfacial pressure term and the virtual mass force, bringing new differential terms to the system can change the previous analysis and make the problem hyperbolic. The case where the two phases are incompressible has been studied by Stuhmiller in 1977, but till now, no proof of their efficiency in rendering the model hyperbolic exists in the compressible case. The aim of this paper is to detail the effects these forces have on the hyperbolicity of the Two-Fluid Model in the compressible case. We characterise the location and topology of the non hyperbolic regions, and propose a closure for the interfacial pressure that makes the system unconditionnally hyperbolic