Investigations of submonolayer films show that phase transition broadening due to in premelting is a general phenomenon. Its experimental observation and thermodynamic interpretation is particularly simple for molecules, which form solid monolayer domains of uniform thickness. This is demonstrated with submonolayer films of two classes of molecules: long chain alkanes and alcohols. The investigations yield quantitative data on the intermolecular interactions within the films at the interface between silica and air for molecular coverages extending over several orders of magnitude. At low surface coverages, we find for the two classes of substances a similar behavior. They behave like 2-dimensional gases. For higher coverages, when the molecules form closed films, the behavior is very different. This is explained by the different molecular organization within the films at higher coverages. The alkanes form a homogeneous, van der Winds-like liquid film with randomly oriented molecules. The alcohols are organized as a closed film with the OH groups oriented toward the silica surface. Thus, the OH group density at the silica/film interface changes with varying coverage. This leads to a change in the OH group hydration, which dominates the interactions between the alcohol molecules. The results demonstrate that the interface-induced premelting can be used as a new and quite universal tool to measure intermolecular interactions within molecularly thin films at solid/vapor interfaces.