The nonlinear rheology of multilayer stacks of alternating isotactic polypropylene (PP) and polyethylene (PE) films with N layers was measured in shear and uniaxial extension. We show that the force to extend N - 1 interfaces can lead to strain hardening. We studied three PE/PP pairs: a Ziegler-Natta catalyzed pair and two metallocene pairs, one with high density PE and one with linear low density PE. Interfacial tension was measured on matrix/droplet blends of each pair using small amplitude oscillatory shear measurements fitted with the Palierne model. Multilayer coextrusion was used to fabricate bilayers and sheets with hundreds of layers for each polyolefin pair. Under shear deformation, disentangling of chains in the N - 1 interfaces led to a decrease in the overall shear viscosity, which is interpreted as an interfacial slip velocity and is in agreement with previous studies on multilayer films. Under extensional flows, the multilayers exhibited an increased transient extensional viscosity (tensile stress growth coefficient, eta(+)(E,M)) and pronounced strain hardening, even when the constituent homopolymers exhibited no strain hardening behavior. A model based on a force summation was developed to predict this behavior with interfacial tension as a fitting parameter; the extracted interfacial tensions agreed reasonably well with those from the Palierne model. The "slip in shear" and "hardening in extension" behaviors highlight the role of interfacial polymer physics during rheological measurements and polymer processing. (C) 2019 The Society of Rheology.