Microfluidic devices can be used to represent industrial and natural mixed extensional-shear flows and to measure, simultaneously, in-situ rheological properties of viscoelastic fluids. However, such measurements are challenging due to the nature of mixed flow kinematics. In this study, we present a new mathematical framework to quantify the extensional behavior of viscoelastic fluids in mixed flows through a hyperbolic contraction-expansion microfluidic device. This approach provides a better estimation of apparent extensional viscosity when the non-Newtonian fluid kinematic does not promote additional flow phenomena such as vortices, shear banding or high-velocity jet. We then apply this approach to analyze the mixed rheology of two different viscoelastic surfactant solutions. The results indicate that there is a critical flow rate where extensional properties of the studied viscoelastic fluids start losing importance possibly due to additional flow phenomena. We also found a viscoelastic transition regime from extensional tension-thickening to tension-thinning as flow rate increases.