By combining interface-sensitive nonlinear magneto-optical experiments with femtosecond time resolution and ab initio time-dependent density functional theory, we show that optically excited spin dynamics at Co/Cu(001) interfaces proceeds via spin-dependent charge transfer and back transfer between Co and Cu. This ultrafast spin transfer competes with dissipation of spin angular momentum mediated by spin-orbit coupling already on sub 100 fs timescales. We thereby identify the fundamental microscopic processes during laser-induced spin transfer at a model interface for technologically relevant ferromagnetic heterostructures.