Frictional contact interfaces play a key role in dynamic behavior of mechanical systems. Various nonlinear mechanisms such as micro slap, micro and macro slippage develop at the frictional interface depending on the vibration amplitude at the contact surface. Majority of experimental studies consider the dynamic characteristics of the contact only in one direction, either tangential or normal. In the present paper, a procedure is proposed in which both components of the contact forces in these directions are simultaneously identified. The paper considers nonlinear behavior of a beam with frictional contact support as an experimental case study. The excitation force is set to dual sine harmonics and the measured responses are expanded using the beam nonlinear modes. This provides a reduced order model of the continuous system under study and forms the bases for identification of restoring forces in the contact interface. The restoring forces are identified using force state mapping technique and the hysteresis loops demonstrating the contact energy dissipation mechanisms are determined. The results demonstrate strong coupling effects between tangential and normal restoring forces and their dominant effects on the nonlinear characteristics of the contact interface in both directions.