The growth of crystalline ice films on Pt(111) and Pd(111) is investigated using temperature programed desorption of the water films and of rare gases adsorbed on the water films. The water monolayer wets both Pt(111) and Pd(111) at all temperatures investigated [e.g., 20-155 K for Pt(111)]. However, crystalline ice films grown at higher temperatures (e.g., T>135 K) do not wet the monolayer. Similar results are obtained for crystalline ice films of D2O and H2O. Amorphous water films, which initially wet the surface, crystallize and dewet, exposing the water monolayer when they are annealed at higher temperatures. Thinner films crystallize and dewet at lower temperatures than thicker films. For samples sputtered with energetic Xe atoms to prepare ice crystallites surrounded by bare Pt(111), subsequent annealing of the films causes water molecules to diffuse off the ice crystallites to reform the water monolayer. A simple model suggests that, for crystalline films grown at high temperatures, the ice crystallites are initially widely separated with typical distances between crystallites of approximately 14 nm or more. The experimental results are consistent with recent theory and experiments suggesting that the molecules in the water monolayer form a surface with no dangling OH bonds or lone pair electrons, giving rise to a hydrophobic water monolayer on both Pt(111) and Pd(111).