This paper presents the results of studying the characteristics of hydrogen sensors based on thin In2O3 films modified with tin and dysprosium with dispersed double Pt/Pd catalysts deposited on the surface. To control the content of Sn and Dy in the films, an original technology was developed, and ceramic targets were fabricated from powders of the In–Dy–O, Dy–Sn–O, and In–Dy–Sn–O systems synthesized by the sol–gel method. Films of complex composition were obtained by RF magnetron sputtering of the corresponding targets. Structural features of the obtained thin films were studied by Raman spectroscopy. It is shown that various combinations of tin and dysprosium concentrations, as well as the presence of Pt/Pd catalysts on the surface, have a significant effect on the defectiveness of the films and the density of oxygen adsorption centers. As a result, the resistance of sensors in pure air (R0), the activation energies of the temperature dependences of R0, the bending of the energy bands at the grain boundaries of the semiconductor, and the responses to the action of hydrogen in the concentration range of 20–25,000 ppm change. A unique feature of Pt/Pd/ In2O3: Sn (0.5 at%), Dy (4.95 at%) films is their high sensitivity at 20–100 ppm and the absence of signal saturation in the region of high hydrogen concentrations of 5000–25,000 ppm, allowing them to be used to detect H2 in a wide range of concentrations.