The resonant desorption of H2O from ice multilayers was studied using a train of picosecond pulses from an infrared free electron laser. The infrared light was used to excite the O-H stretching vibration in H2O in the ice multilayers and to cause H2O resonant desorption. The H2O resonant desorption spectrum was measured at infrared wavelengths between lambda = 2.8 mu m and lambda = 3.4 mu m. The peak H2O desorption yield occurred at lambda = 3.0 mu m. The H2O resonant desorption spectrum was substantially enhanced relative to the infrared absorption spectrum of ice at infrared wavelengths shorter than lambda similar to 3.1 mu m. This enhancement was attributed to the melting of the ice film prior to H2O desorption and the temperature-dependent absorption coefficient of the O-H stretching vibration. The H2O desorption yields from 1 and 5 mu m thick films were also measured at lambda = 2.94 mu m and lambda = 3.09 mu m for successive infrared pulses and versus pulse energy. The results were consistent with the melting of the ice film and the expected optical penetration depths in liquid water. Model calculations were in qualitative agreement with these experimental results and predicted H2O desorption from a liquid H2O film.