Atomic force microscopy (AFM) was used to study the growth and morphology of ice films on the cleavage surface of mica. Measurements performed in contact, as well as in noncontact operation modes of the microscope, allowed us to distinguish the solid and liquid parts of the film. At temperatures below -30 degrees C, supercooled water droplets formed on top of a thin (nanometer range) ice layer in contact with the substrate. After annealing, a contiguous flat film was formed. Between -20 and -10 degrees C and at a relative humidity of similar to 83%, the film consisted of a solid ice layer similar to 7 Angstrom thick, covered by a liquid-like layer 50 +/- 5 Angstrom thick. When the temperature was raised above 0 degrees C, droplets formed, which subsequently evaporated. Comparison of results obtained in the various AFM operation modes allowed us to conclude the existence of a liquid-like layer on the ice surface.