Studies have been carried out to increase the adhesive interaction between a titanium hydride substrate and a copper coating. An additional layer containing chemically active groups was created on the surface of the spherical titanium hydride by chemisorption modification. This paper discusses the results of scanning electron microscopy (SEM) using energy-dispersive X-ray spectroscopic mapping of coatings obtained on spherical granules of titanium hydride before and after adsorption modification. The mechanism of interaction of the surface of spherical granules of titanium hydride and titanium sulfate salt is proposed. It is shown that the creation of a chemisorbed layer of hydroxotitanyl and the subsequent electrodeposition of metallic copper contribute to the formation of a multilayer shell of a titanium–copper coating on the surface of spherical titanium hydride granules (≡Ti-O-Cu-) with a high adhesive interaction. Results have been given for an experimental study of the thermal stability of the initial spherical granules of titanium hydride and granules coated with a multilayer titanium-copper shell.