We present a new model of the nebular emission from star-forming galaxies in a wide range of chemical compositions, appropriate to interpret observations of galaxies at all cosmic epochs. The model relies on the combination of state-of-the-art stellar population synthesis and photoionization codes to describe the ensemble of H ii regions and the diffuse gas ionized by young stars in a galaxy. A main feature of this model is the self-consistent yet versatile treatment of element abundances and depletion on to dust grains, which allows one to relate the observed nebular emission from a galaxy to both gas-phase and dust-phase metal enrichment. We show that this model can account for the rest-frame ultraviolet and optical emission-line properties of galaxies at different redshifts and find that ultraviolet emission lines are more sensitive than optical ones to parameters such as C/O abundance ratio, hydrogen gas density, dust-to-metal mass ratio and upper cut-off of the stellar initial mass function. We also find that, for gas-phase metallicities around solar to slightly subsolar, widely used formulae to constrain oxygen ionic fractions and the C/O ratio from ultraviolet and optical emission-line luminosities are reasonable faithful. However, the recipes break down at non-solar metallicities, making them inappropriate to study chemically young galaxies. In such cases, a fully self-consistent model of the kind presented in this paper is required to interpret the observed nebular emission.