The results of a spectroscopic programme aiming to investigate the kinematics of the local interstellar medium components towards the Southern Coalsack and Chamaeleon-Musca dark clouds are presented. The analysis is based upon high-resolution (R ~ 60,000) spectra of the insterstellar NaI D absorption lines towards 63 B-type stars (d < 500 pc) selected to cover these clouds and the connecting area defined by the Galactic coordinates: 308 > l > 294 and -22 < b < 5. The radial velocities, column densities, velocity dispersions, colour excess and photometric distances to the stars are used to understand the kinematics and distribution of the interstellar cloud components. The analysis indicates that the interstellar gas is distributed in two extended sheet-like structures permeating the whole area, one at d < 60 pc and another around 120-150 pc from the Sun. The dust and gas feature around 120-150 pc seem to be part of an extended large scale feature of similar kinematic properties, supposedly identified with the interaction zone of the Local and Loop I bubbles.