To improve mobile robot positioning accuracy in building environments and construct structural three-dimensional (3D) maps, this paper proposes a stereo visual-inertial odometry (VIO) system based on structural lines and points belonging to lines. The 2-degree-of-freedom (DoF) spatial structural lines based on the Manhattan world assumption are used to establish visual measurement constraints. The property of point belonging to a line (PPBL) is used to initialize the structural lines and establish spatial distance-residual constraints between point and line landmarks in the reconstructed 3D map. Compared with the 4-DoF spatial straight line, the 2-DoF structural line reduces the variables to be estimated and introduces the orientation information of scenes to the VIO system. The utilization of PPBL makes the proposed system fully exploit the prior geometric information of environments and then achieves better performance. Tests on public data sets and real-world experiments show that the proposed system can achieve higher positioning accuracy and construct 3D maps that better reflect the structure of scenes than existing VIO approaches.