  Far Ultraviolet Spectroscopic Explorer (FUSE) data is used to investigate the
molecular hydrogen (H_2) content of intermediate-velocity clouds (IVCs) in the
lower halo of the Milky Way. We analyze interstellar absorption towards 56
(mostly extragalactic) background sources to study H_2 absorption in the Lyman-
and Werner bands in 61 IVC components at H I column densities >10^19 cm^-2. For
data with good S/N (~9 per resolution element and higher), H_2 in IVC gas is
convincingly detected in 14 cases at column densities varying between ~10^14
and ~10^17 cm^-2. We find an additional 17 possible H_2 detections in IVCs in
FUSE spectra with lower S/N. The molecular hydrogen fractions, f, vary between
10^-6 and 10^-3, implying a dense, mostly neutral gas phase that is probably
related to the Cold Neutral Medium (CNM) in these clouds. If the H_2 stays in
formation-dissociation equlibrium, the CNM in these clouds can be characterized
by compact (D~0.1 pc) filaments with volume densities on the order of n_H~30
cm^-3. The relatively high detection rate of H_2 in IVC gas implies that the
CNM in these clouds is ubiquitous. More dense regions with much higher
molecular fractions may exist, but it would be difficult to detect them in
absorption because of their small size.
