The pressure between the layers of the pleura is negative due to the following reasons:
The tendency of the lungs and thoracic wall to recoil in the opposite direction expands the intrapleural space and creates negative pressure i.e. below the atmospheric pressure in between the two layers of pleura. Ref: Fundamentals of Respiratory Physiology By A. S. Chakrabay, Chakrabay, 2007, Page 33
The thoracic wall and lungs recoil in opposite directions
Intra pulmonary pressure is negative
Trans pulmonary pressure is negative
The surfactant prevents the pulmonary collapse