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 \approx 60 000 ) spectra of the insterstellar NaI D absorption lines towards 63 B-type stars ( d \leq 500 pc ) selected to cover these clouds and the connecting area defined by the Galactic coordinates : 308 \degr \geq l \geq 294 \degr and -22 \degr \leq b \leq 5 \degr . 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 \leq 60 pc and another around 120-150 pc from the Sun . The nearby feature is approaching to the local standard of rest with average radial velocity of - 7 km s ^ { -1 } , has low average column density log N _ { Na { \mbox { \sc i } } } \approx 11.2 cm ^ { -2 } and velocity dispersion b \approx 5 km s ^ { -1 } . The more distant feature has column densities between 12.3 \leq log N _ { Na { \mbox { \sc i } } } \leq 13.2 , average velocity dispersion b \approx 2.5 km s ^ { -1 } and seems associated to the dust sheet observed towards the Coalsack , Musca and Chamaeleon direction . Its velocity is centered around 0 km s ^ { -1 } , but there is a trend for increasing from - 3 km s ^ { -1 } near b = 1 \degr to 3 km s ^ { -1 } near b = -18 \degr . The nearby low column density feature indicates a general outflow from the Sco-Cen association , in aggreement with several independent lines of data in the general searched direction . 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 . Assuming that the interface and the ring-like volume of dense neutral matter that would have been formed during the collision of the two bubbles have similar properties , our results rather suggest that the interaction zone between the bubbles is twisted and folded .