We consider a new C₂H nanostructure based on bilayer graphene transformed under the covalent bond of hydrogen atoms adsorbed on its external surface, as well as compounds of carbon atoms located opposite each other in neighboring layers. They constitute a “film” of the 〈111〉 diamond with a thickness of less than 1 nm, which is called diamane. The energy characteristics and electron spectra of diamane, graphene, and diamond are calculated using the density functional theory and are compared with each other. The effective Young’s moduli and destruction thresholds of diamane and graphene membranes are determined by the molecular dynamics method. It is shown that C₂H diamane is more stable than CH graphane, its dielectric “gap” is narrower than the band gap of bulk diamond (by 0.8 eV) and graphane (by 0.3 eV), and is harder and more brittle than the latter.