Diffuse and translucent molecular clouds provide rigorous tests of theories of interstellar chemistry and of cloud structure because they can be observed both through UV/visible/IR absorption lines and radio- frequency emission lines. We propose to fill in some crucial missing information through ISO spectroscopy on IR emission lines of [C II], [O I], and H_2. These data will provide direct constraints on the cooling and thermal structure of these molecular clouds, which are thin enough that their chemistry and ionization are mostly photon-dominated. Most of these clouds are thought not to be bound by their own self- gravity, which means that effects of pressure are significant. Moreover their low densities, 100-1000 cm^-3, imply that one is more likely to see observable manifestations of turbulence on their chemistry and thermal structure than in the denser clouds where turbulence is damped out on smaller scales. Our target list has been selected according to two criteria. First, the targets are all clouds for which we have already obtained extensive ground-based data on optical absorption lines and mm-wave emission lines. Second, the lines of sight to these clouds are relatively uncontaminated by foreground or background matter and the observed line profiles are typically simple. Even so, the target list includes clouds with a variety of properties: clouds closely associated with shocks, isolated clouds, clouds whose abundances are primarily atomic, and clouds with well developed molecular abundances. The observations will be interpreted with reference to detailed theoretical models. The ISO data will provide direct tests of our understanding of the thermal structure and of some aspects of the chemistry of photon-dominated regions (PDRs), of which our clouds are simple examples.