Hi Frederick, so what you're running into there is that boolean union will merge together faces with planes that are coplanar fragments of a larger plane and also surfaces that share the same "underlying surface" under their trimming boundaries.
That merging is normally helpful for modeling but it is getting in the way of your current goal of keeping the face structure intact.
Right now there isn't any way to turn off that behavior in the booleans but there are other ways you can achieve the end result you want.
The first way is to delete the common faces so the pieces are open there, like this (here I deleted the top face of the bottom piece, you would also need to delete the bottom face of the upper piece):
Then when you have pieces with open edges that are all touching each other you can use Edit > Join to glue them together. Unlike the booleans, the join command does not try to do any cutting of material nor any merging of faces, it only joins naked edges to other naked edges.
The other way to approach it would be to make it all one solid piece and then cut it with a line drawn in a side view using the Edit > Trim command with the "Keep all joined" option at the last stage. That will slice up the "skin" of a solid but still keep it all connected together.
Hope this helps!
- Michael
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