This paper deals with the analysis of a class of implicit variational inequalities which generalizes some dynamic contact problems coupling adhesion and friction between two viscoelastic bodies of Kelvin-Voigt type. Existence and uniqueness results are proved for a general system of evolution inequalities that constitutes a unified approach to study some complex dynamic surface interactions, including rebonding, debonding and friction conditions. The proofs are based on incremental formulations, several estimates, compactness arguments and a fixed point technique. These results are applied to dynamic frictional contact conditions with reversible adhesion and the coefficient of friction depending on the slip velocity.