Mixed-dimensional magnetic heterostructures are intriguing, newly available platforms to explore quantum physics and its applications. Using state-of-the-art many-body perturbation theory, we predict the energy level alignment for a self-assembled monolayer of cobalt phthalocyanine (CoPc) molecules on magnetic VSe 2 monolayers. The predicted projected density of states on CoPc agrees with experimental scanning tunneling spectra. Consistent with experiment, we predict a shoulder in the unoccupied region of the spectra that is absent from mean-field calculations. Unlike the nearly spin-degenerate gas phase frontier molecular orbitals, the tunneling barriers at the interface are spin-dependent, a finding of interest for quantum information and spintronics applications. Both the experimentally observed shoulder and the predicted spin-dependent tunneling barriers originate from many-body interactions in the interface-hybridized states. Our results showcase the intricate many-body physics that governs the properties of these mixed-dimensional magnetic heterostructures, and suggests the possibility of manipulating the spin-dependent tunneling barriers through modifications of interface coupling.