In an earlier paper [J. Sadler, B. O'Neill, and R. Maev, J. Acoust. Soc. Am. 118, 51-59 (2005)], a set of generalized boundary conditions were proposed, based on a thin layer (thickness << wavelength) model of the acoustic interface. In this paper, the model is extended to cover the more pathological nonlinearity of the adhesion interphase-that is, the critically important thin layer where bonds are formed between adhesive and substrate. First, the boundary conditions are shown to be sufficiently general to cope with all manner of interphase nonlinearity, including unilateral cases such as clapping or slipping. To maintain this generality, an analytic time domain solution is proposed based on expansion in terms of the layer thickness rather than the conventional expansion in terms of harmonics. Finally, the boundary conditions are applied to an interphase failure model based upon basic continuum damage mechanics principles. It is proposed that such a model, which can predict the evolution of the interphase damage under stressful conditions, may allow a proper prediction of the ultimate adhesion strength based on nonlinear parameters measured nondestructively with ultrasound.