We report on the use of graphene templating to investigate the room-temperature structure and dynamics of weakly bound adlayers at the interfaces between solids and vapors of small organic molecules. Monolayer graphene sheets are employed to preserve and template molecularly thin adlayers of tetrahydrofuran (THF) and cyclohexane on atomically flat mica substrates, thus permitting a structural characterization of the adlayers under ambient conditions through atomic force microscopy. We found the first two adlayers of both molecules adsorb in a layer-by-layer fashion, and atomically flat two-dimensional islands are observed for both the first and the second adlayers. THF adlayers form initially as rounded islands but, over a period of weeks, evolve into faceted islands, suggesting that the adlayers possess both liquid and solid properties at room temperature. Cyclohexane adlayers form crystal-like faceted islands and are immobile under the graphene template. The heights of the second adlayers of THF and cyclohexane are measured to be 0.44 +/- 0.02 and 0.50 +/- 0.02 nm, respectively, in good agreement with the layer thicknesses in the monoclinic crystal structure of THF and the Phase I "plastic crystal" structure of cyclohexane. The first adlayers appear slightly thinner for both molecules, indicative of interactions of the molecules with the mica substrate.