Welcome to our Forum. Have you applied for a copy of the official service record of your Father as yet ? How to do so can be found below You may wish to contact the RM Museum, they have a Historical Society, about an indepth history of MNBDO11 in Sicily, or arrange a visit to the National Archives to view War Diaries.
After Sicily many would become part of Combined Operations but certainly not all would have become Commandos.
The Royal Marines Museum have this at the end of their entry for MNBDO11:
After service on detached duties with the Eighth Army, the units of MNBDO II were assembled in Augusta (Sicily) for embarkation and arrived in the UK in February 1944 the HQ was disbanded in May 1944 and personnel of all but those AA Regiments forming 5 RM AA Bde were sent to North Wales for selection as landing craft crews, commandos or for other duties.