The objective of this paper is to propose a time integration scheme for nonsmooth mechanical systems involving one-sided contact, impact and Coulomb friction, that respects the principles of discretetime energy balance with positive dissipation. To obtain energetic consistency in the continuous time model, we work with an impact law inspired by the work of M. Frémond (Frémond, 2001, 2002, 2017) which ensures that dissipation is positive, i.e. that the Clausius-Duhem inequality is satisfied. On this basis, we propose a time integration method based on the Moreau-Jean scheme (Jean and Moreau, 1987; Moreau, 1988) and show that this method has correct dissipation properties.