We have performed self-consistent calculations to study the interlayer exchange coupling and transport properties of FM/Os/FM trilayers (FM = Co, Fe, FeCo and FePt) as a function of the osmium spacer thickness. Our results are in a good agreement with the published experimental results. The antiferromagnetic (AF) coupling observed experimentally in trilayers where Os spacer thickness was 9-10 angstrom and where the ferromagnetic slabs were Fe, Co and FeCo verify very well our calculated results. For FePt/Os/FePt, we have attributed the AF coupling peak observed experimentally at a one monolayer (1 ML) Os spacer thickness to our calculated AF coupling at 1 ML in a disordered magnetic layer and, by introducing the effect of the interface roughness in our calculations, we found that the peak is shifted towards 1.5 ML. We fitted our interlayer exchange coupling (IEC) results to an Ruderman-Kittel-KasuyaYosida (RKKY) function to the third order to obtain the periods of oscillations and their strengths quantitatively. We have found in a Co/Os/Co trilayer that the values of the oscillation periods of the IEC are 4 and 7 ML; the latter was observed experimentally. Due to the lack of experimental data for the periods of oscillations in FeCo/Os/FeCo, Fe/Os/Fe and FePt/Os/FePt, we compared our results to another method of calculation and found good agreement. An enhancement in the giant magnetoresistance (GMR) is observed for an ordered ferromagnetic slab compared to systems with a disordered ferromagnetic slab.