Military
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor
Flight Crew Last 90 Days 40; Flight Crew Total 2800; Flight Crew Type 40
Confusion; Distraction; Situational Awareness; Training / Qualification
Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Took Evasive Action
Airspace Structure; Chart Or Publication; Human Factors
While approaching 7NM initial at ZZZ AFB under Runway Supervisory Unit ops control; my 3 ship of military aircraft were told that tower was going to have control of the runway for commercial traffic at 20 mile final.  My 3 ship were instructed to carry through the overhead and go around the pattern.  We executed that and once we were 90 to initial at 2;800 feet we picked up the visual to a commercial aircraft (Aircraft Y) approximately 200 feet above and descending to the runway..  I initiated the turn to initial early and offset the runway to the west to avoid the commercial aircraft.  During the turn my wing men got perhaps 3;000 feet from me and they were not squawking in accordance with with our procedures.  I was told that Aircraft Y had previously gone around and this was their second attempt to land. I was also told they received a TCAS advisory. I do not recall hearing a TCAS advisory; however my system was on 'TA' and it is very common to receive multiple traffic advisories in the pattern.  I believe they were flying the RNAV Approach that does not have a hard altitude of 2300 feet at the final approach fix; like the ILS and TACAN approach does.  We do that to avoid the VFR pattern traffic at 2800. I would suggest a review of all approaches at ZZZ AFB to avoid this situation again; or for the commercial traffic to have been assigned a hard altitude of 2300 feet until Final Approach Fix.
Military Pilot reported an airborne conflict in the traffic pattern.