Abstract We have complemented existing observations of H i absorption with new observations of HCO⁺, C₂H, HCN, and HNC absorption from the Atacama Large Millimeter/submillimeter Array and the Northern Extended Millimeter Array in the directions of 20 background radio continuum sources with 4° ≤ ∣b∣ ≤ 81° to constrain the atomic gas conditions that are suitable for the formation of diffuse molecular gas. We find that these molecular species form along sightlines where A _V ≳ 0.25, consistent with the threshold for the H i-to-H₂ transition at solar metallicity. Moreover, we find that molecular gas is associated only with structures that have an H i optical depth >0.1, a spin temperature <80 K, and a turbulent Mach number ≳ 2. We also identify a broad, faint component to the HCO⁺ absorption in a majority of sightlines. Compared to the velocities where strong, narrow HCO⁺ absorption is observed, the H i at these velocities has a lower cold neutral medium fraction and negligible CO emission. The relative column densities and linewidths of the different molecular species observed here are similar to those observed in previous experiments over a range of Galactic latitudes, suggesting that gas in the solar neighborhood and gas in the Galactic plane are chemically similar. For a select sample of previously observed sightlines, we show that the absorption line profiles of HCO⁺, HCN, HNC, and C₂H are stable over periods of ∼3 yr and ∼25 yr, likely indicating that molecular gas structures in these directions are at least ≳100 au in size.