The Amex Bank and Discover Bank are separate corporations and while there's money flowing to/from these banks in a variety of ways, it's not like the Visa/MC - Bank relationships.
Hmm, apparently American Express Co. sold off American Express Bank last year. I didn't know that.
Discover is unique since Discover Bank is part of Discover Financial Services, but I don't believe that it's owned by DFS. However, since pretty much all Discover Cards are issued by Discover Bank, if Discover Bank suddenly went belly up and totally stopped operations, then pretty much everyone's Discover Card in their wallets would presumably be useless at that point because there's no issuing bank.