Lipid composition dictates membrane thickness, which in turn can influence membrane protein activity. Lipid composition also determines whether a membrane demixes into coexisting liquid-crystalline phases. Previous direct measurements of demixed lipid membranes have always found a liquid-ordered phase that is thicker than the liquid-disordered phase. Here we investigated noncanonical ternary lipid mixtures designed to produce bilayers with thicker disordered phases than ordered phases. The membranes were composed of short, saturated (ordered) lipids; long, unsaturated (disordered) lipids; and cholesterol. We found that few of these systems yield coexisting liquid phases above 10 °C. For membranes that do demix into two liquid phases, we measured the thickness mismatch between the phases by atomic force microscopy and found that not one of the systems yields thicker disordered than ordered phases under standard experimental conditions. We found no monotonic relationship between demixing temperatures of these ternary systems and either estimated thickness mismatches between the liquid phases or the physical parameters of single-component membranes composed of the individual lipids. These results highlight the robustness of a membrane's liquid-ordered phase to be thicker than the liquid-disordered phase, regardless of the membrane's lipid composition.