We investigated the strong antiferromagnetic (AF) interlayer exchange coupling (IEC) at junctions between Fe(001) and Fe3O4(001) epitaxial films and the effects of an insertion layer of Mn or Co. In addition, we developed a nonlinear least-squares-fit technique to analyze the details of the magnetization processes and to distill the IEC constants. The analyses were performed by taking into account bilinear and biquadratic exchange couplings with a twisted magnetization state. The fitting results suggest the existence of significant distributions in bilinear and/or biquadratic IECs, which can originate from nonuniform stacking of atoms at the interface. The insertion of a Co layer with a thickness in the range of zero to two monolayers between the Fe3O4(001) and the Fe(001) layers significantly affects the magnetic-hysteresis (M-H) processes, whereas the insertion of a Mn layer does not. A quantitative fitting analysis of M-H curves suggests that the inserted thin Mn layer does not affect the AF-IEC significantly, whereas the Co layer suppresses the AF coupling and in fact is preferable for achieving ferromagnetic coupling, which is consistent with the tendency predicted by our theoretical model regarding impurity effects for the IEC of Fe/Fe3O4(001).