I just had a similar question about Delta interlining policy with Etihad. I called up Delta and the representative said that as long as Delta has interlining agreements with Etihad they will check the baggage to the final destination. And the rep did confirm that Delta has interline agreements with Etihad. Print both your tickets with confirmation number and PNR and show it at the check in counter.
I will post my experience in ~ 4 days.