To find an alternative way for improving the efficacy of deep eutectic solvents (DESs) to dissolve carbon dioxide, a computational study of DES systems comprising choline chloride and different hydrogen-bond donors (ethylene glycol and glycerol) immobilized on hydrophobic (graphite) and hydrophilic (titanium dioxide) solid surfaces was performed. This research provides quantitative molecular understanding of the role of the DES thickness and also the type of solid support in CO2 sorption and diffusion using molecular dynamics simulations. In general, the proposed model based on supported DESs immobilized on different supports was developed to correlate the solubility of CO2 in DESs based on choline chloride. The simulated systems illustrate that CO2 molecules mainly accumulate at the gas/DES interface in short times, whereas diffusion of CO2 to the bulk DESs is slower as the thickness of the immobilized DES increases. In addition, the CO2 absorption capacity of both DESs coated on the TiO2 surface is larger than that on the graphite surface. Structural and dynamic characteristics were determined using density profiles, distribution functions, orientational analysis, and mean-square displacements. We further demonstrate the effective interaction parameters associated with CO2 capture by DESs via density functional theory.