Using the surface forces apparatus, we have measured the static and hydrodynamic forces between two substrate supported lipid bilayers in water and semidilute aqueous solutions of 8000 MW poly(ethylene glycol) (PEG), a neutral polymer for which water is a good solvent. At small separations (D < R-F, Flory radius), an enhanced adhesion due to depletion attraction was measured. Conversely, at larger separations we found a repulsive barrier, which is not predicted by mean-field theories. Dynamic measurements of the viscosity as a function of film thickness reflected the same pattern of behavior as exhibited in the static force experiments : Thus, in the absence of polymer, the shear plane was at the lipid-water interface, while in the 8000 MW polymer solution the viscosity decreased as a function of decreasing surface separation due to a polymer-depleted layer of lower viscosity at the bilayer surface. We discuss our results in terms of depletion attraction, depletion stabilization, thin film lubrication, the effective viscosity in thin films, and the possibility of polymer aggregates in PEG solutions. The crossover from depletion attraction to adsorption and repulsion with increasing MW is addressed in part 2 of this work.