We combine data from our recent FUSE survey of interstellar molecular hydrogen absorption toward 50 high-latitude AGNs with COBE-corrected IRAS 100 μm emission maps to study the correlation of infrared cirrus with H2. A plot of the H2 column density versus IR cirrus intensity shows the same transition in molecular fraction, fH2, as seen with total hydrogen column density, NH. This transition is usually attributed to H2 ``self-shielding,'' and it suggests that many diffuse cirrus clouds contain H2 in significant fractions, fH2~1%-30%. These clouds cover ~50% of the northern sky at b>30deg, at temperature-corrected 100 μm intensities DT100>=1.5 MJy sr-1. The sheetlike cirrus clouds, with hydrogen densities nH>=30 cm-3, may be compressed by dynamical processes at the disk-halo interface, and they are conducive to H2 formation on grain surfaces. Exploiting the correlation between NH2 and 100 μm intensity, we estimate that cirrus clouds at b>30deg contain ~3000 Msolar in H2. Extrapolated over the inner Milky Way, the cirrus may contain 107 Msolar of H2 and 108 Msolar in total gas mass. If elevated to 100 pc, their gravitational potential energy is ~1053 ergs.