Surface structures and related electronic properties of flat Co nanoislands supported on Cu(1 1 1) are studied before and after adsorbing different doses of molecular hydrogen at 10 K by low-temperature scanning tunneling microscopy/spectroscopy (STM/STS) at 5 K. It is found that the adsorption process on Co consists in two steps. First, H2 dissociatively chemisorbs on Co forming an atomic H adlayer. Subsequently, molecules impinging on that H-terminated Co surface are physisorbed. When adsorbing a low dose of hydrogen on the Co/Cu(1 1 1) system, STM analysis shows that the chemisorbed hydrogen adlayer on Co forms a p(2 × 2) superstructure. On Cu surface however, no superstructure is observed. When adsorbing a high dose of H2, hydrogen-induced superstructures are observed on both Co and Cu surfaces. These superstructures are ascribed to the presence of physisorbed molecules as revealed by the STS spectra. A (3 × 3) superstructure is observed on Co and a mixture of (2 × 2) and (3 × 3) is identified on Cu. A model describing the adsorption sites of molecules is proposed: H2 molecules occupy on-top sites when arranged as a (2 × 2) phase and they occupy on-top and bridge sites when arranged as a (3 × 3) phase. Besides, STM-induced desorption is used to desorb atomic hydrogen from selected Co nanoisland surface. The desorption is visualized in terms of a disappearance of the p(2 × 2) superstructure.