Join paths while preserving all lines
I'm very new to Illustrator, so a big part of my problem is that I don't know all the names, expressions and possibilities yet, which makes it really hard to search for answers. Sorry if some of my expressions are wrong, and please do correct me if something doesn't make sense.
I'm trying to make some simple line work, and I'd like to be able to join multiple paths together while preserving all the lines.

In the attached image I'm trying to join two rectangle shapes, so that the bottom corner merges, instead of having two intersecting corners as in the image.
But when I use Pathfinder -> Join the line in the middle (marked with pink) disappears. This is of course because the two shapes are merged into one, so the line in the middle is no longer an outline.
How can I join the two shapes together while preserving this line?
And quite possible this is not even the way to achieve the artwork I want to do, so in case there is a better way than joining two shapes, please let me know ![]()
