The gas at the surfaces of molecular clouds in galaxies is heated and dissociated by photons from young stars both near and far. HI resulting from the dissociation of molecular hydrogen H2 emits hyperfine line emission at 21 cm, and warmed CO emits dipole rotational lines such as the 2.6 mm line of CO(1-0). We use previously developed models for photodissociation regions (PDRs) to compute the intensities of these HI and CO(1-0) lines as a function of the total volume density n in the cloud and the far ultraviolet flux G0 incident upon it and present the results in units familiar to observers. The intensities of these two lines behave differently with changing physical conditions in the PDR, and, taken together, the two lines can provide a ground-based radio astronomy diagnostic for determining n and G0 separately in distant molecular clouds. This diagnostic is particularly useful in the range Gzero <~ 100, 10 cm^{-3} <~ n <~ 10^5 cm^{-3}, which applies to a large fraction of the volume of the interstellar medium in galaxies. If the molecular cloud is located near discrete sources of far-UV (FUV) emission, the PDR-generated HI and CO(1-0) emission on the cloud surface can be more easily identified, appearing as layered ``blankets or ``blisters on the side of the cloud nearest to the FUV source. As an illustration, we consider the Galactic object G216 -2.5, i.e. ``Maddalenas Cloud, which has been previously identified as a large PDR in the Galaxy. We determine that this cloud has n ~ 200 cm^{-3}, G0 ~ 0.8, consistent with other data.
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