No, but the sender had a contract with them, to deliver the package, not USPS. USPS were acting as a subcontractor in this instance. So legally DHL are liable if anyone is.
I guarantee you the contract you have with shipping companies doesn't let you (successfully) sue them simply because the package didn't get delivered. No shipping company would still exist today if that were the case, they would have been sued into the ground long ago.
