Drainage of water from the region between an advancing probe tip and a flat sample is reconsidered under the assumption that the tip and sample surfaces are both coated by a thin water "interphase" (of width approximately a few nanometers) whose viscosity is much higher than that of the bulk liquid. A formula derived by solving the Navier-Stokes equations allows one to extract an interphase viscosity of similar to59 kPa(.)s (or similar to6.6 x 10(7) times the viscosity of bulk water at 25 degreesC) from interfacial force microscope measurements with both tip and sample functionalized hydrophilic by CH-terminated tri(ethylene glycol) undecylthiol, self-assambled monolayers.