How can I invert the direction of blocks in a structure?
It depends on how close they need to be.

The following solution works, if you're happy to have things sticking out around the join:

"Brick 1x2 M. 2 Holes Ø 4,87", [part:32000:7]; There's also a 1x1 brick with a hole, [part:6541:7].

Which could be used as:



For tighter coupling, the Minifig Wrench [part:6246d:0] can also fit over a stud, and is deeper than one stud, allowing two bricks to be inserted:



Respect goes to Erik Amzallag for this one.

I guess it comes down to how you want to hide the join - you could use tiles on the studs that stick out, which wouldn't be possible with the wrench method.