To date, most of the studies dealing with the magnetic properties of 4f-3d compounds have been limited to the case in which the 4f ion was Gd-III, with a pure spin ground state. For the lanthanide(III) ions with a first-order orbital momentum, the determination of the nature of the 4f-3d interaction is still a challenge. This paper addresses this problem. The magnetic properties of the compounds of formula {Ln(2)[M(opba)](3)}. S (abbreviated hereafter as Ln(2)M(3)) have been investigated; Ln stands for a lanthanide element, M for Cu or Zn, opba for ortho-phenylenebis-(oxamato), and S for solvent molecules. All of these compounds have similar one-dimensional structures consisting of ladder-type motifs. Our approach consisted of comparing the magnetic properties of Ln(2)Cu(3) and Ln(2)Zn(3) for each Ln(III) ion. The former are governed by both the thermal population of the Stark components of Ln(III) and the Ln(III)-Cu-II interaction; the latter are only governed by the thermal population of the Ln(III) Stark components. It has been confirmed that the Gd-III-Cu-II interaction was ferromagnetic, and it was found that the Tb-III-Cu-II and Dy-III-Cu-II interactions were ferromagnetic as well. The Tm-III-Cu-II interaction might also be ferromagnetic; the situation, however, is uncertain. On the other hand, in all other cases the Ln(III)-Cu-II interaction is not ferromagnetic; it is either not detectable by the magnetic technique or antiferromagnetic. The difference between Dy-III-Cu-II (ferromagnetic) and Ho-III-Cu-II (not ferromagnetic) is particularly striking. These findings have been discussed.