Ultrasonic waves are useful tools to characterize the contact forces between components in non-destructive and non-invasive manners. It has been shown that the transmission and reflection coefficients of the ultrasonic wave are sensitive to the contact pressure or other contact parameters. Theoretically, the normal and tangential stiffnesses of the contact interface govern the transmission/reflection coefficients and can be used as parameters to characterize the contact condition. However, weak and incomplete interfaces, formed by rough surfaces in partial contact, show a highly nonlinear behaviour also when they are excited under free vibrations. In particular, the amplitude of the second harmonic is a relevant index of the contact stiffness, and the nonlinear response is strongly influenced by the nominal contact pressure applied to the boundaries. In this study a new theoretical model of the nonlinear interface stiffness was developed where the stiffness of the contact interface was described as a function of the nominal contact pressure. The developed theoretical contact pressure function of the second harmonic generation at the contact interface was found to agree with good accuracy with the experimental data. Moreover, this paper presents also a theoretical and experimental study aimed at developing an integrity index capable of assessing the stiffness of the contact interface between structures when excited by free vibration or under controlled vibration excitation.