Finite linear spaces consisting of two symmetric configurations

We investigate finite linear spaces consisting of two symmetric configurations. A construction method using projective planes is presented, giving a possibly infinite number of examples. Other examples are constructed by difference families and automorphism groups, including a complete classification of the smallest case. A question whether any Steiner 2-design with twice as many lines as points belongs to this family of linear spaces is raised, and answered in the affirmative for all known examples of such designs.