Great Lakes (http://www.flygreatlakes.com) used to fly a Miles City - Denver route but they have been replaced by Gulfstream International (http://www.gulfstreamair.com) as Montana's Essential Air Service carrier. Gulfstream flies a Miles City to Billings route.
As far as I know, there is no commercial airline service directly between Miles City and Denver. You'll have to charter a plane or fly to Billings on Gulfstream and then fly to Denver from there on a different airline.