Much of the short-range forces and structures of softly supported DMPC bilayers has been described previously. However, one interesting feature of the measured force-distance profile that remained unexplained is the presence of a long-range exponentially decaying repulsive force that is not observed between rigidly supported bilayers on solid mica substrate surfaces. This observation is discussed in detail here based on recent static and dynamic surface force experiments. The repulsive forces in the intermediate distance regime (mica-mica separations from 15 to 40 nm) are shown to be due not to an electrostatic force between the bilayers but to compression (deswelling) of the underlying soft polyelectrolyte layer, which may be thought of as a model cytoskeleton. The experimental data can be fit by simple theoretical models of polymer interactions from which the elastic properties of the polymer layer can be deduced.