Carbon monoxide (CO) is a poor tracer of H_2_ in the diffuse interstellar medium (ISM), where most of the carbon is not incorporated into CO molecules, unlike the situation at higher extinctions. We present a novel, indirect method for constraining H_2_ column densities (NH_2_) without employing CO observations. We show that previously recognized nonlinearities in the relation between the extinction, AV(H_2_), derived from dust emission and the HI column density (NHI) are due to the presence of molecular gas. We employed archival NH_2_ data, obtained from the UV spectra of stars, and calculated AV(H_2_) toward these sight lines using 3D extinction maps. A third-degree polynomial fits the data well and can be used to estimate NH_2_ using NHI and AV(H_2_). In 95% of the cases, the estimates produced by the fitted equation have deviations of less than a factor of 3.5. We constructed a NH_2_ map of our Galaxy and compared it to the CO integrated intensity (W_CO_) distribution. We find that the average ratio (X_CO_) between NH_2_ and W_CO_ is approximately equal to 2x10^20cm^-2^(K.km/s)^-1^, consistent with previous estimates. However, we find that the XCO factor varies by orders of magnitude on arcminute scales between the outer and the central portions of molecular clouds. For regions with NH_2_>=10^20^cm^-2^, we estimate that the average H_2_ fractional abundance is 0.25. Multiple (distinct) largely atomic clouds are likely found along high-extinction sightlines (AV>=1mag), hence limiting fH_2_ in these directions. More than 50% of the lines of sight with NH_2_>=10^20cm^-2^ are untraceable by CO with a J=1-0 sensitivity limit WCO=1K.km/s.