Infrared reflection-absorption spectroscopy is used to investigate thin (1-200 Angstrom average thickness) overlayers of D2O ice deposited in ultrahigh vacuum on controlled wettability self-assembled monolayers. The monolayers were derived from mixed solutions of HS(CH2)(15)CH3 and HS(CH2)(16)OH, making it possible to examine the whole range of samples from f(OH) = 0.0 to f(OH) 1.0, where f(OH) denotes the molar fraction of OH-terminated thiols in the preparation solution. This paper focuses on the interaction between the ice and the monolayer. It is shown that water molecules do not penetrate into the monolayer but that two types of interaction with the chain-terminating groups occur: hydrogen bond formation with surface hydroxyls and weak dipole-dipole interaction with surface methyls. For surfaces with f(OH) < 0.3, the latter interaction causes the free OD mode, normally observed at 2729 cm(-1), to shift to 2704 cm(-1), thereby providing a spectral signature feature whose intensity is directly proportional to the relative area of the ice/monolayer interface. Quantitative analysis of the infrared spectra suggests that ice clusters are essentially flat on surfaces with 0.6 < f(OH) < 1.0 and become more droplet-like for decreasing f(OH) below 0.6. On f(OH) = 0.0 surfaces, the microscopic clusters display high contact angles (similar to 120 degrees), and full surface coverage does not occur until the average overlayer thickness is 150-200 Angstrom.