A series of 3d-4f binuclear complexes, [M(3-MeOsaltn)(MeOH)x(ac)Ln(hfac)2] (x = 0 for M = Cu(II), Zn(II); x = 1 for M = Co(II), Ni(II); Ln = Gd(III), Tb(III), Dy(III), La(III)), have been synthesized and characterized, where 3-MeOsaltn, ac, and hfac denote N,N'-bis(3-methoxy-2-oxybenzylidene)-1,3-propanediaminato, acetato, and hexafluoroacetylacetonato, respectively. The X-ray analyses demonstrated that all the complexes have an acetato- and diphenolato-bridged M(II)-Ln(III) binuclear structure. The Cu(II)-Ln(III) and Zn(II)-Ln(III) complexes are crystallized in an isomorphous triclinic space group P1, where the Cu(II) or Zn(II) ion has square pyramidal coordination geometry with N2O2 donor atoms of 3-MeOsaltn at the equatorial coordination sites and one oxygen atom of the bridging acetato ion at the axial site. The Co(II)-Ln(III) and Ni(II)-Ln(III) complexes are crystallized in an isomorphous monoclinic space group P2(1)/c, where the Co(II) or Ni(II) ion at the high-spin state has an octahedral coordination environment with N2O2 donor atoms of 3-MeOsaltn at the equatorial sites, and one oxygen atom of the bridged acetato and a methanol oxygen atom at the two axial sites. Each Ln(III) ion for all the complexes is coordinated by four oxygen atoms of two phenolato and two methoxy oxygen atoms of "ligand-complex" M(3-MeOsaltn), four oxygen atoms of two hfac(-), and one oxygen atom of the bridging acetato ion; thus, the coordination number is nine. The temperature dependent magnetic susceptibilities from 1.9 to 300 K and the field-dependent magnetization up to 5 T at 1.9 K were measured. Due to the important orbital contributions of the Ln(III) (Tb(III), Dy(III)) and to a lesser extent the M(II) (Ni(II), Co(II)) components, the magnetic interaction between M(II) and Ln(III) ions were investigated by an empirical approach based on a comparison of the magnetic properties of the M(II)-Ln(III), Zn(II)-Ln(III), and M(II)-La(III) complexes. The differences of χ(M)T and M(H) values for the M(II)-Ln(III), Zn(II)-Ln(III) and those for the M(II)-La(III) complexes, that is, Δ(T) = (χ(M)T)(MLn) - (χ(M)T)(ZnLn) - (χ(M)T)(MLa) = J(MLn)(T) and Δ(H) = M(MLn)(H) - M(ZnLn)(H) - M(MLa)(H) = J(MLn)(H), give the information of 3d-4f magnetic interaction. The magnetic interactions are ferromagnetic if M(II) = (Cu(II), Ni(II), and Co(II)) and Ln = (Gd(III), Tb(III), and Dy(III)). The magnitudes of the ferromagnetic interaction, J(MLn)(T) and J(MLn)(H), are in the order Cu(II)-Gd(III) > Cu(II)-Dy(III) > Cu(II)-Tb(III), while those are in the order of M(II)-Gd(III) ≈ M(II)-Tb(III) > M(II)-Dy(III) for M(II) = Ni(II) and Co(II). Alternating current (ac) susceptibility measurements demonstrated that the Ni(II)-Tb(III) and Co(II)-Tb(III) complexes showed out-of-phase signal with frequency-dependence and the Ni(II)-Dy(III) and Co(II)-Dy(III) complexes showed small frequency-dependence. The energy barrier for the spin flipping was estimated from the Arrhenius plot to be 14.9(6) and 17.0(4) K for the Ni(II)-Tb(III) and Co(II)-Tb(III) complexes, res...