I am spending way too much time on this! After some encouragement by other OSM contributors, I started to verify the map data of the area I live/work in. While doing so, it occured to me that there must be some way to map/tag something like an underpass to make the renderer draw it correctly. To my surprise, I did not find much on this topic in my favorite wiki pages (Map features and Proposed features) and a quick search revealed only some old email discussion (see http://lists.openstreetmap.org/pipermail/talk/2006-January/002215.html). I guess I somehow have to find out if the elevated tag mentioned there is really the way to go or if there is some other way to map multiple road levels.