A model is developed to describe the charge transfer-induced spin transition in a crystal containing cyanide-bridged binuclear Co-Fe clusters as a structural element. The model accounts for the electronic states arising from two cluster configurations active in the transition and, namely, from the ground ls-CoIII-ls-FeII and the excited hs-CoII-ls-FeIII ones. The cooperative interaction that originates from the coupling of the acoustic crystalline modes with the molecular vibrations describing the displacements of the nearest ligand surroundings of the metal ions is assumed to be responsible for spin transformation. The problem of interacting clusters is solved within mean field approximation. The role of the order parameters is played by the mean values of the products of the electronic matrices and coordinates of the molecular vibrations in the ground and excited cluster configurations. The developed model provides quite a reasonable description of the observed temperature dependence of the magnetic characteristics of the [{(Tp)Fe(CN)3}{Co-(PY5Me2)}](CF3SO3)⋅2DMF complex. The factors controlling the electron transfer in this complex are elucidated.