A commercial ceria–zirconia composition modified with yttrium and lanthanum oxides was studied as a support for palladium- and rhodium-containing three-way catalysts. The most attention was paid to an interaction of the supported active metals with the support under high-temperature conditions. It was found that both the metals affect noticeably the porous structure of the support and the loading of metal plays a role in this process. Moreover, oxygen storage capacity of the oxide composition was also influenced by the supported metals. Hydrothermal aging of the metal-loaded samples has decreased the oxygen storage capacity values in more than 2 times. The thermal stability of the monometallic samples was compared with bimetallic Pd–Rh catalysts prepared using a “single-source precursor” approach. The experiments were performed under prompt thermal aging conditions. It was found that monometallic Pd-only samples and bimetallic Pd–Rh samples exhibit excellent stability, while monometallic Rh-only catalysts undergo deactivation being heated up to 800 °C due to diffusion of rhodium into the bulk of the support. All the samples were additionally characterized by a diffuse reflectance UV–vis spectroscopy and a testing reaction of ethane hydrogenolysis. According to the results obtained, the character of the metal-support interaction was found to be strongly affected by the catalyst’s composition. Application of the bimetallic Pd–Rh particles of alloyed type was shown to result in the preferable location of the active components on the support’s surface, thus facilitating high activity and stability of the catalyst.