We have studied the fluoride-bridged Dy-Cr molecular nanomagnet [Dy(hfac)4-CrF2(py)4]·1/2CHCl3 by x-ray magnetic circular dichroism (XMCD). The obtained element-specific magnetization curves allow for a quantification of the sign and strength of the magnetic exchange coupling between the Dy and the Cr ions. In an effective spin-1/2 formalism only taking into account the ground Kramers doublet of the DyIII ion, we find a coupling strength of jeff,z = -2.3(1) cm-1. Further, we find that the ground Kramers doublet is nearly perfectly axial with geff,z,Dy = 19.6(6) and geff,xy,Dy = 0(2). The coupling value corresponds to a "true", non-effective isotropic coupling of j = -0.16 cm-1 when taking into account a full J = 15/2 angular momentum. This coupling strength is comparable to that of j = -0.18 cm-1 previously found in the related fluoride-bridged compound Dy-Cr-Dy.