The paper deals with the well-posedness of the time-dependent Stokes–Darcy model for an incompressible fluid in a bounded domain. The no-leak boundary condition and a multivalued nonmonotone slip condition of “friction type” is assumed. The latter is governed by the generalized subgradient of a locally Lipschitz superpotential. The transmission conditions across the interface boundary involve a new frictional boundary condition, which is proposed as a generalization of the popular Beavers–Joseph–Saffman law. The weak formulation of the problem is a parabolic hemivariational inequality for the Stokes velocity and the Darcy pressure. The well-posedness of the model is established under suitable assumptions involving a smallness condition.