We studied the effect of a solid surface on the fluid-fluid phase separation of a colloid-polymer mixture in real space, exploring demixing from both the unstable and metastable regions of the phase diagram. The presence of a wall breaks the symmetry of the phase separation morphology in the direction perpendicular to the surface, influencing the coarsening behavior of domains. We analyzed the thickening of the wetting layers and found that hydrodynamic transport processes can significantly increase the rate of wetting-layer growth. Depending on the volume ratio between the two phases, a new regime was observed in which the demixing structure disconnected from the wall, but remained bicontinuous in the bulk. We also discuss the effect of a crossover in the demixing regime of bulk domains on the growth of this layer.