[en] The effect of interfacial coupling on rectification in an organic co-oligomer spin diode is investigated theoretically by considering spin-independent and spin-resolved couplings respectively. In the case of spin-independent coupling, an optimal interfacial coupling strength with a significant enhanced rectification ratio is found, whose value depends on the structural asymmetry of the molecule. In the case of spin-resolved coupling, we found that only the variation of the interfacial coupling with specific spin is effective to modulate the rectification, which is due to the spin-filtering property of the central asymmetric magnetic molecule. A transition of the spin-current rectification between parallel spin-current rectification and antiparallel spin-current rectification may be observed with the variation of the spin-resolved interfacial coupling. The interfacial effect on rectification is further analyzed from the spin-dependent transmission spectrum at different biases. (paper)