The Martian regolith is the most substantial volatile reservoir on the planet; estimates of its adsorbed inventory have been based on simple measurements of the adsorption of either water or CO2 in isolation. Under some conditions, H2O can poison adsorbate surfaces, such that CO2 uptake is greatly reduced. We have made the first measurements of the simultaneous adsorption of CO2 and H2O under conditions appropriate to the Martian regolith and have found that at H2O monolayer coverage above about 0.5, CO2 begins to be displaced into the gas phase. We have developed an empirical expression that describes our co-adsorption data and have applied it to standard models of the Martian regolith. We find that currently, H2O does not substantially displace CO2, implying that the adsorbate inventories previously derived may be accurate, not more than 3--4 kPa (30--40 mbar). No substantial increase in atmospheric pressure is predicted at higher obliquities because high-latitude ground ice buffers the partial pressure of H2O in the pores, preventing high monolayer coverages of H2O from displacing CO2. The peak atmospheric pressure at high obliquity does increase as the total inventory of exchangeable CO2 increases.