First principles calculations reveal that the effects of PbBi on the cohesive properties of Fe3O4 and (Fe,Cr)3O4: PbBi can reduce the cohesive strength of the oxides, and the contents of O and Cr on the O-terminated oxide side play a significant role in the cohesive properties of the PbBi/Fe3O4 and PbBi/(Fe,Cr)3O4 interfaces. Specifically, the performance of oxidation decreases more significantly under the conditions of insufficient oxygen, and a high ratio of Cr of the subsurface of oxides can lead to the reduction of the cohesive properties of O-terminated interfaces. Calculations also show that the Pb-O-terminated interfaces are energetically favorable and are more stable than the Bi-O-terminated surfaces due to the strong bond of Pb-O, while the Bi-Cr and Bi-Fe interfaces are more stable than the Pb-Cr and Pb-Fe interfaces. Moreover, it is found that the stability and cohesion of the PbBi/Fe3O4 and PbBi/(Fe,Cr)3O4 interfaces will decrease when the oxygen concentration is insufficient or the degree of wetting of PbBi of oxides is low, and the PbBi/Fe3O4 interface is more sensitive to these conditions. The bond-dissociation energies and electronic structures provide a deep understanding of various interface properties, and the obtained results are in good agreement with experimental measurements in the literature.