In-depth clarification of hydrogen interaction with noble metal nanoparticles and nanoalloys is essential for further development and design of efficient catalysts and hydrogen storage nanomaterials. This issue becomes even more challenging for nanoalloys of bulk-immiscible metals. The hydrogen interaction with bulk-immiscible Pd-Rh nanoalloys (3-6 nm) supported on mesoporous carbon is studied by both laboratory and large scale facility techniques. X-ray diffraction (XRD) reveals a single phase fcc structure for all nanoparticles confirming the formation of nanoalloys in the whole composition range. In situ extended x-ray absorption fine structure (EXAFS) experiments suggest segregated local structures into Pd-rich surface and Rh-rich core coexisting within the nanoparticles. Hydrogen sorption can be tuned by chemical composition: Pd-rich nanoparticles form a hydride phase, whereas Rh-rich phases do not absorb hydrogen under ambient temperature and pressure conditions. The thermodynamics of hydride formation can be tailored by the composition without affecting hydrogen capacity at full hydrogenation. Furthermore, for hydrogen absorbing nanoalloys, in situ EXAFS reveals a preferential occupation of hydrogen for the interstitial sites around Pd atoms. To our knowledge, this is the first study providing insights into the hydrogen interaction mechanism with Pd-Rh nanoalloys that can guide the design of catalysts for hydrogenation reactions and the development of nanomaterials for hydrogen storage.