Neutron reflectivity studies of EuS/SrS, EuS/PbSe and EuS/PbTe all-semiconductor superlattices were carried out in a search for exchange interlayer coupling. A relatively weak antiferromagnetic coupling was found in EuS/SrS and EuS/PbSe systems but no interlayer coupling was detected in EuS/PbTe superlattices. In EuS/SrS, where the SrS spacer is an insulator (E(g)≈4 eV), a very weak and short range interlayer coupling is in agreement with the earlier theoretical predictions that the interlayer coupling strength in EuS-based magnetic semiconductor superlattices depends strongly on the energy gap of the nonmagnetic layer and should decrease with an increase of the energy gap of the spacer material. A weak coupling in EuS/PbSe and no coupling in EuS/PbTe, where both PbSe and PbTe are narrow-gap semiconductors (E(g)≈0.3 eV), is in disagreement not only with the theoretical expectations but also in stark contrast with earlier results for another narrow-gap spacer system, EuS/PbS, where pronounced antiferromagnetic coupling persists even in samples with PbS layer thicknesses as large as 200 Å. A possible influence of the increasing lattice mismatch between EuS and the spacer materials (0.5%, 0.8%, 2.5% and 8.2% for PbS, SrS, PbSe and PbTe, respectively) on the magnetic ordering of the EuS layer near the interfaces and, consequently, on the interlayer coupling is discussed.