We study the interpenetration of a polymer solution placed on top of a colloidal suspension. Direct observations show that at the interface, the depletion attraction induced by the polymer causes the colloids to aggregate in a thin layer. This acts as a semipermeable membrane, through which the polymer osmotic pressure squeezes out solvent from the colloidal suspension like a cafetiere plunger. Observations using fluorescent polymers show that despite the very high concentration gradients present, very little of the polymer gets into the colloid. The movement of the colloid-polymer interface has two regimes at increasing initial polymer concentration. First, the interface moves at a constant velocity with a constant thickness. In this regime, the interfacial velocity does not depend on the initial colloid volume fraction but increases linearly with the polymer osmotic pressure (Pi(p)). We show that these observations are consistent with Darcy-type flow through the interfacial membrane driven by Pi(p). At higher polymer concentration, a strong instability occurs and the interfacial layer breaks and reforms regularly. The origin of this nonlinear behavior is unclear. The relationship of our observations to fouling in ultrafiltration in an unstirred batch cell is discussed.