  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. ``Maddalena's 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.
