We present a study of high-velocity gas in the direction of 13 halo sub-dwarfs located at absolute value of z approximately equals 0.5-2 kpc and of 8 early-type stars in the Galactic disk at d approximately equals 1-4 kpc. For each line of sight of our sample we collected Ca II and Na I absorption spectra with the 2.5-m Isaac Newton Telescope at La Palma (Spain) and H I 21-cm emission profiles with the 100-m radiotelescope at Effelsberg (Germany). The faint sub-dwarfs (mv approximately equals 11-14) are observed for the first time at relatively high spectral resolution (approximately equals 25-30 km/s) in the optical. By comparing the optical absorptions (or upper limits) with the 21-cm emissions, we constrain the distances to the concentrations of neutral gas at high velocity named Complex C, Complex H, and for high velocity gas located between the Cohen Stream and the Magellanic Stream. We find new evidence for gas at intermediate velocity in the halo and in the disk of our Galaxy.