A thermodynamic model for estimating the saturation conditions of H2O–CO2 mixed fluids in multicomponent silicate liquids is described. The model extends the capabilities of rhyolite-MELTS (Gualda et al. in J Petrol 53:875–890, 2012a) and augments the water saturation model in MELTS (Ghiorso and Sack in Contrib Mineral Petrol 119:197–212, 1995). The model is internally consistent with the fluid-phase thermodynamic model of Duan and Zhang (Geochim Cosmochim Acta 70:2311–2324, 2006). It may be used independently of rhyolite-MELTS to estimate intensive variables and fluid saturation conditions from glass inclusions trapped in phenocrysts. The model is calibrated from published experimental data on water and carbon dioxide solubility, and mixed fluid saturation in silicate liquids. The model is constructed on the assumption that water dissolves to form a hydroxyl melt species, and that carbon dioxide both a molecular species and a carbonate ion, the latter complexed with calcium. Excess enthalpy interaction terms in part compensate for these simplistic assumptions regarding speciation. The model is restricted to natural composition liquids over the pressure range 0–3 GPa. One characteristic of the model is that fluid saturation isobars at pressures greater than ~100 MPa always display a maximum in melt CO2 at nonzero H2O melt concentrations, regardless of bulk composition. This feature is universal and can be attributed to the dominance of hydroxyl speciation at low water concentrations. The model is applied to four examples. The first involves estimation of pressures from H2O–CO2-bearing glass inclusions found in quartz phenocrysts of the Bishop Tuff. The second illustrates H2O and CO2 partitioning between melt and fluid during fluid-saturated equilibrium and fractional crystallization of MORB. The third example demonstrates that the position of the quartz–feldspar cotectic surface is insensitive to melt CO2 contents, which facilitates geobarometry using phase equilibria. The final example shows the effect of H2O and CO2 on the crystallization paths of a high-silica rhyolite composition representative of the late-erupted Bishop Tuff. Software that implements the model is available at ofm-research.org, and the model is incorporated into the latest version (1.1+) of rhyolite-MELTS.