@Lara

Still just a simple Boolean, just with an offset object...

Instead of trying to "melt" 2 objects together, try 3. Space them apart, insert the bridge object you want, Boolean the whole kittenkaboodle and then fillet to desired width.

Goes like this: Draw your first box object, rotate it holding the CTRL key (gives you a copy). Move the boxes where you normally would, only leave space for twice the fillet size you want, then make a bridge object to match (another box). You now have three boxes which you need to "Boolean Unite" and then fillet. Done..