The measurement of interfacial mechanical or rheological properties in polymer blends is a challenging task, as well as providing a quantitative link between these properties and the interfacial nanostructure. Here, we perform a systematic study of the extensional rheology of multilayer films of an immsicible polymer pair, polystyrene and poly(methyl methacrylate). We take advantage of multinanolayer coextrusion to increase the number of interfaces up to thousands, consequently magnifying the interfacial response of the films. The transient elongational response is compared to an addivity rule model based on the summation of the contribution of each polymer as well as the interfacial one. At low strain rates, the model reproduces the transient extensional viscosity up to strain-thinning, while at larger ones, the extra stress exceeds the prediction based on constant interfacial tension. This extra-contribution is attributed to an interphase modulus on the order of 1-10 MPa, which increases with strain rate following a power-law with an exponent 1/3. Extensional rheology of multinanolayer films is then an efficient combination to go beyond interfacial tension and measure quantitatively the interfacial rheology of immiscible polymer blends.