I believe the structural rigidity of the box structure of two wings was also a factor.
Sure, that makes sense, and you can even experience it on a kit: on a biplane, when only the lower wings are attached to the fuselage, they are pretty fragile. When the upperwing and masts are installed, the whole structure is much more rigid, and it gets even better when the rigging is on.
Monoplanes required a lot of bracing and rigging; biplane wings could be lighter with each supporting the other by struts and less rigging.
In the end, you have more lift for less drag with a biplane. Of course, things changed when engineers were able to build strong enough cantilever wings. In the thirties, there were still a debate about what was more important: maneuverability of the biplane formula, or speed of the cantilever monoplane architecture. In the end, the I-16 and Bf109 put an end to this debate during the Spanish Civil War.