In the present work, a polymeric transient viscoelastic network is used as a model system to investigate several fundamentals of interfacial viscoelasticity and nonlinear behavior, in simple shear, compression, and for simple mixed deformations. A supramolecular polymer bilayer, characterized by long but finite relaxation times, is created at the water-air interface using a layer-by-layer assembly method. The possibility of studying the individual layers starting from an unstrained reference state enabled the independent quantification of the equilibrium thermodynamic properties, and the viscoelastic response of the bilayer could be studied separately for shear and compressional deformations. Time- and frequency-dependent material functions of the layer were determined in simple shear and uniform compression. Moreover, a quasilinear neo-Hookean model for elastic interfaces was adapted to describe step strain experiments on a viscoelastic system by allowing the material properties to be time-dependent. The use of this model made it possible to calculate the response of the system to step deformations. Within the linear response regime, both stress-strain proportionality and the superposition principle were investigated. Furthermore, the onset of nonlinear behavior of the extra stresses was characterized in shear and for the first time in pure compression. We conclude by investigating the multilayer system in a rising bubble setup and show that the neo-Hookean model is able to predict the extra and deviatoric surface stresses well up to moderate deformations. (C) 2019 The Society of Rheology.