This comes from a video made by the European Resistance Archive: https://www.youtube.com/watch?v=TSqEETgU1h4.
He says only that he was with a Russian when he fought in small battle in a village in Italy. No other context is given but this made me wonder how often a foreign-born person might have fought with other armies of other countries. I understand this might be very difficult to answer but would appreciate anything.
The Royal Air Force incorporated personnel from around the world, both within regular squadrons and national squadrons. The latter were formed under the Allied Forces Act from personnel from occupied countries (Polish, Czech, French, Norwegian, Dutch, Belgian, Greek and Yugoslav squadrons) and Article XV of the British Commonwealth Air Training Plan from Dominions (Canadian, Australian and New Zealand squadrons).
As you mention Italy and partisans, one of the most polyglot air units I'm aware of was the Balkan Air Force (BAF). Established in June 1944 with headquarters at Bari, the BAF co-ordinated Allied operations in the Balkans, particularly supporting and supplying Tito's partisans in Yugoslavia. Its combat strength featured, at various points, seven regular RAF squadrons, two Yugoslav RAF squadrons, three Greek RAF squadrons, three South African Air Force squadrons, seven Gruppo of the Italian Co-Belligerent Air Force, and (nominally, at least) a Soviet VVS squadron flying Yak-9DD fighters. Transport aircraft of 334 (Special Duties) Wing came from the RAF (some with Polish pilots) and USAAF, and the VVS also provided a squadron of Dakotas for a time.
The Soviet presence was most unusual, a rare instance of Soviet forces operating under British control, though BAF command was rather nominal; they "asked much and gave little" according to the official history. Their Dakotas flew around 400 sorties, escorted by the Yaks from Bari, supporting the Soviet military mission in Yugoslavia. The rest of the BAF operated until VE Day, major operations including RATWEEK in September 1944, hitting transportation targets to hinder German redeployment following the surrender and change of allegiance of Romania.
For more details of the BAF see Chapter XI of The Royal Air Force 1939-1945, Volume III: The Fight is Won, Hilary St. George Saunders, and Jeff Jefford's The Balkan Air Force in Journal 46 of the RAF Historical Society.