The role of interphase triggered from interdiffusion process at neighboring layers on controlling the interfacial flow instability of multilayer coextrusion have been highlighted in this study using a compatible bilayer system. The polymers used are based on poly(methyl methacrylate) (PMMA) and poly(vinylidene fluoride) (PVDF). The interdiffusion kinetics and the rheological and geometrical properties of the generated interphase have been modelized in real experimental conditions of the coextrusion process. Polymer chain orientation in coextrusion process was demonstrated to decelerate the interdiffusion coefficient. Furthermore, the interfacial shear stress was able to promote mixing and homogenizing process at the vicinity of the interface, which favors the development of the interphase. The convective mixing was evidenced by performing a pre-shear mode on PMMA/PVDF multilayer structures. The rheological and morphological properties of the interphase are related to a lot of parameters like contact time, processing temperature, interfacial shear stress and compatibility of the polymers, etc. Some key classical decisive parameters concerning the interfacial instability phenomena such as viscosity ratio, thickness ratio and elasticity ratio, etc. were highlighted during the coextrusion process. These key factors which are significant for the interfacial stability of coextrusion of incompatible multilayered polymers seem not that important for the studied compatible systems. The coextrusion of PMMA/PVDF compatible bilayers appears to be more stable. This would be attributable to the presence of the interphase generated from interdiffusion and favored from convective mixing. The interfacial flow instability of coextrusion can be reduced (or even eliminated) despite of the very high viscosity ratio and elasticity ratio of PMMA versus PVDF, especially at low temperatures. Overall, apart from the classical mechanical parameters, we have demonstrated that the creation of diffuse interphase that favors the homogenization should be taken into consideration as an important factor to remove the interfacial instability properties.