The interface exchange coupling between ferromagnetic (F) and antiferromagnetic (AF) materials is interesting in itself and has also attracted recent attention in relation to the exchange bias phenomenon. A major difficulty in developing a reliable exchange bias theory lies in the fact that both the F and AF interface characteristics (geometry and physical parameters) are hard to determine experimentally and complicated to estimate theoretically. We adopt in this paper two alternative interface configurations to obtain upper and lower bounds for the computed values of the exchange coupling across the interface between metallic Fe and insulating FeF₂, derived on the basis of ab-initio calculations implemented for a periodic supercell. Electronic structures and total energies were computed within density functional theory (DFT) using the generalized gradient approximation (GGA) for the exchange correlation potential. We expect the results obtained to be useful in model simulations with larger unit cells and non-collinear spins.