We present the results of experiments aimed at studying the interaction of hydrogen atoms at 80 K with carbon grains covered with a water ice layer at 12 K. The effects of H processing have been analyzed, using IR spectroscopy, as a function of the water ice layer. The results confirm that exposure of the samples to H atoms induces the activation of the band at 3.47 μm with no evidence for the formation of aromatic and aliphatic C-H bonds in the CH2 and CH3 functional groups. The formation cross section of the 3.47 μm band has been estimated from the increase of its integrated optical depth as a function of the H atom fluence. The cross section decreases with increasing thickness of the water ice layer, indicating an increase of adsorption of H atoms in the water ice layer. A penetration depth of 100 nm has been estimated for H atoms in the porous water ice covering carbon grains. Sample warm-up at room temperature causes the activation of the IR features due to the vibrations of the CH2 and CH3 aliphatic functional groups. The evolution of the 3.47 μm band carrier has been evaluated for dense and diffuse interstellar clouds, using the estimated formation cross section and assuming that the destruction cross section by energetic processing is the same as that derived for the 3.4 μm band. In both environments, the presence of the 3.47 μm band carrier is compatible with the evolutionary timescale limit imposed by fast cycling of materials between dense and diffuse regions of the interstellar medium. In diffuse regions the formation of the CH2 and CH3 aliphatic bands, inhibited in dense regions, takes place, masking the 3.47 μm band. The activation of the CH2 and CH3 aliphatic vibrational modes at the end of H processing after sample warm-up represents the first experimental evidence supporting an evolutionary connection between the interstellar carbon grain population, which is responsible for the 3.4 μm band (diffuse regions) and contributes to the absorption at 3.47 μm (dense regions), and the organics observed in interplanetary dust particles and cometary Stardust grains.