Those eligible for the military room discount are also eligible to purchase the dining plan on a ticketless package. Annual passholders have the same opportunity. Nobody else does, except for some occasional offers made to Disney cast members. When you call, say you want the military room plus dining package. (This is still a package and is subject to the same deposit, change and cancellation policies as other packages.)
(DVC reservations don't count as room plus dining packages - DVC doesn't book packages at all)