The problem of the kinetic exchange interaction in the cyanide-bridged heterobinuclear dimers involving orbitally degenerate transition metal ions is considered. The developed approach is based on the concept of the effective Hamiltonian of the orbitally dependent kinetic exchange. We deduce this many-electron Hamiltonian on the microscopic background so that all relevant biorbital transfer processes are taken into account as well as the properties of the many-electron states. The bioctahedral cyanide-bridged Cr(III)Fe(II) dimer is considered in detail as an example distinctly exhibiting new quantitative and qualitative features of the orbitally dependent exchange and as a structural unit of three-dimensional ferromagnetic crystals {Fe(II)(3)[Cr(III)(CN)(6)](2)}.13H(2)O. The proposed mechanism of the kinetic exchange involves the electron transfer from the double occupied t(2) orbitals of Fe(II) [ground state T-5(2)(t(2)(4)e(2))] to the half occupied t(2) orbitals of Cr(III) [ground state (4)A(2)(t(2)(3))] resulting in the charge transfer state T-3(1)(t(2)(4))(Cr(II))-(6)A(1)(t(2)(3)e(2))(Fe(III)) and the transfer between the half-occupied t(2) orbitals of the metal ions resulting in the charge transfer state T-3(1)(t(2)(4))(Cr(II))-T-4(2)(t(2)(3)e(2))(Fe(III)). The effective Hamiltonian of the orbitally dependent exchange for the Cr(III)Fe(II) pair deduced within this theoretical framework describes competitive ferro-and antiferromagnetic contributions arising from these two charge transfer states. This Hamiltonian leads to a complex energy pattern, consisting of two interpenetrating Heisenberg-like schemes, one exhibiting ferromagnetic and another one antiferromagnetic splitting. The condition for the ferromagnetic spin alignment in the ground state is deduced. The orbitally dependent terms of the Hamiltonian are shown to give rise to a strong magnetic anisotropy of the system, this result as well as the condition for the spin alignment in the ground term are shown to be out of the scope of the Goodenough-Kanamori rules. Along with the full spin S the energy levels are labeled by the orbital quantum numbers providing thus the direct information about the magnetic anisotropy of the system. Under a reasonable estimation of the excitation energies based on the optical absorption data we conclude that the kinetic exchange in the cyanide-bridged Cr(III)Fe(II) pair leads to the ferromagnetic spin alignment exhibiting at the same time strong axial magnetic anisotropy with C-4 easy axis of magnetization.