My girlfriend is a foreigner with german residence card. Upon returning from trips, we were told by german border police that she can enter Germany with onlyand while I advise her residence card, just like a EU citizen. We successfully tried thisto take her passport on subsequentall our trips, she almost never needs to show it unless we cross a non-Schengen border.
On flights within the EU, passports or ID cards are rarely checked at all. Even less so on national flights. At HAM, which I've used regularily, ID is rarely requested for national flights, but I've seen it happen (not to individuals, rather a "please show your passport and boarding pass when boarding" announcement).
So practically, you should be fine. That doesn't mean the airline can not cause you trouble, either legally or illegally. Many people have been denied entry into Schengen countries, sued and won. So to be certain, you should ask the airline, in writing, and get a written response that you carry with you.