Far Ultraviolet Spectroscopic Explorer (FUSE) data are used to investigate the molecular hydrogen (H2) content of intermediate-velocity clouds (IVCs) in the lower halo of the Milky Way. We analyze interstellar absorption toward 56 (mostly extragalactic) background sources to study H2 absorption in the Lyman and Werner bands in 61 IVC components at H I column densities ≥1019 cm-2. For data with good signal-to-noise ratio (S/N) (~9 per resolution element and higher), H2 in IVC gas is convincingly detected in 14 cases at column densities varying between ~1014 and ~1017 cm-2. We find an additional 17 possible H2 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 H2 stays in formation-dissociation equilibrium, the CNM in these clouds can be characterized by compact (D ~ 0.1 pc) filaments with volume densities on the order of nH ~ 30 cm-3. The relatively high detection rate of H2 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.