If all 4 segments are on one ticket, the baggage allowance for your first segment (IAD-FRA) will continue for the remaining three segments. Has nothing to do with individual carriers or *A. It's a DOT rule.

That said, you may find outstation contract staff on the return won't honor the first segment rule. Don't get a fight because you won't win (on the spot). Pay and then contest the charge, attaching your itinerary and the DOT rule when you are back and the itinerary is complete.