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We study the metallicity dependence of the H/H$_2$ and C$^+$/C/COdistributions in a self-regulated interstellar medium (ISM) across a broadrange of metallicities ($0.1 < Z/Z_\odot < 3$). To this end, we conducthigh-resolution (particle mass of $1\ {\rm M_\odot}$) hydrodynamicalsimulations coupled with a time-dependent H$_2$ chemistry network. The resultsare then post-processed with an accurate chemistry network to model theassociated C$^+$/C/CO abundances, based on the time-dependent non-steady-state(``non-equilibrium'') H$_2$ abundances. We find that the time-averaged starformation rate and the ISM structure are insensitive to metallicity. The columndensities relevant for molecular shielding appear correlated with the volumedensities in gravitationally unstable gas. As metallicity decreases, H$_2$progressively deviates from steady state (``equilibrium'') and shows shallowabundance profiles until they sharply truncate at the photodissociation fronts.In contrast, the CO profile is sharp and controlled by photodissociation as COquickly reaches steady state. We construct effective one-dimensional cloudmodels that successfully capture the time-averaged chemical distributions insimulations. At low metallicities, the steady-state model significantlyoverestimates the abundance of H$_2$ in the diffuse medium. The overestimatedH$_2$, however, has little impact on CO. Consequently, the mass fraction ofCO-dark H$_2$ gas is significantly lower than what a fully steady-state modelpredicts. The mass ratios of H$_2$/C$^+$ and H$_2$/C both show a weakerdependence on $Z^{\prime}$ than H$_2$/CO, which potentially indicates thatC$^+$ and C could be alternative tracers for H$_2$ at low $Z^{\prime}$ in termsof mass budget. Our chemistry code for post-processing is publicly available.

Metallicity dependence of the H/H$_2$ and C$^+$/C/CO distributions in a resolved self-regulating interstellar medium