We present a study of ro-vibrational OH and CO emission from 21 disks around Herbig Ae/Be stars. We find that the OH and CO luminosities are proportional over a wide range of stellar ultraviolet luminosities. The OH and CO line profiles are also similar, indicating that they arise from roughly the same radial region of the disk. The CO and OH emission are both correlated with the far-ultraviolet luminosity of the stars, while the PAH luminosity is correlated with the longer wavelength ultraviolet luminosity of the stars. Although disk flaring affects the PAH luminosity, it is not a factor in the luminosity of the OH and CO emission. These properties are consistent with models of UV-irradiated disk atmospheres. We also find that the transition disks in our sample, which have large optically thin inner regions, have lower OH and CO luminosities than non-transition disk sources with similar ultraviolet luminosities. This result, while tentative given the small sample size, is consistent with the interpretation that transition disks lack a gaseous disk close to the star.