Modeling and identification of restoring forces at contact interfaces is an inevitable part of investigating the dynamic characteristics of mechanical systems. As the vibration amplitude increases, various nonlinear mechanisms such as micro/macro-slip and micro-impacts activate in the interface. This paper considers the nonlinear behavior of a frictional contact in situations where micro-impacts develop in the normal direction to the friction surface. It investigates the effect of variable normal load on the contact frictional forces, and defines a friction model capable of taking into account this effect. In an experimental case study, the contact is excited using a dual sine force to allow a reliable dual-mode identification procedure. The measured data and the normal modes of the corresponding linear system are employed to define the system nonlinear modes used to expand the system response. This provides a reduced order model containing dominant nonlinear effects in the contact interface. Force state mapping method is employed to identify the contact restoring forces. The experimentally obtained forces are employed to determine the parameters of a new friction law defied by modifying the Valanis model. It is shown the model is capable of predicting the main nonlinear characteristics of the contact interface and regenerates the experimental results at different vibration response levels.