Combine data and geometry from vector layers without merging

I have 3 line type vector layers representing municipal infrastructure; sanitary, storm, and water main pipes. Each of these layers should remain separate and all of these layers have different fields, but some common attributes.

I’m trying to create a single atlas that looks at a few of the common attributes between the 3 layers to highlight missing information to present to the client; I don’t want to merge the tables to do so or create 3 separate atlases.

I’ve created a virtual layer that selects the proper information from each table and provides the results in a single table – but unless there’s something I’m missing, I cannot include any geometry in the virtual layer, and therefore my atlas doesn’t work.