We present a quantitative study of the current–voltage characteristics (CVC) of SFIFS Josephson junctions (S = bulk superconductor, F = metallic ferromagnet, I = insulating barrier) with weak ferromagnetic interlayers in the diffusive limit. The problem is solved in the framework of the nonlinear Usadel equations. We consider the case of a strong tunnel barrier such that the left SF and the right FS bilayers are decoupled. We calculate the density of states (DOS) in SF bilayers using a self-consistent numerical method. Then we obtain the CVC of corresponding SFIFS junctions, and discuss their properties for different set of parameters including the thicknesses of ferromagnetic layers, the exchange field, and the magnetic scattering time. We observe an anomalous nonmonotonic CVC in case of weak ferromagnetic interlayers, which we attribute to DOS energy dependencies in the case of small exchange fields in the F layers.