We present confocal microscopy experiments on the wetting of phase-separated colloid-polymer mixtures. We observe that an unusually thick wetting layer of the colloid-rich phase forms at the walls of the glass container that holds the mixture. Because of the ultralow interfacial tension between the colloid-rich and the polymer-rich phases, the thermally activated roughness of the interfaces becomes very big and measurable. We observe that close to the critical point the roughness of the interface between the wetting layer and the polymer-rich phase decreases with decreasing layer thickness: large excursions of the interface are confined in the wetting layer. The measured relationship between the roughness and the thickness of the wetting layer is in qualitative agreement with the predictions of renormalization group theory for short-range forces and complete wetting.