For the US, the answer is that the overwhelming majority of soldiers and marines saw combat (assuming they did see combat) in a single theatre.

For the 6 Marine divisions, they all deployed to the Pacific exclusively. For the 89 U.S. Army divisions, only a very few deployed to the Mediterranean theatre then moved to the European theatre. The full list is: 82nd Airborne, 2nd Armored, 1st Infantry, 3rd Infantry, 9th Infantry, 36th Infantry, 45th Infantry. I make that 7 divisions total. That's out of 95 total divisions.

So if we count by division, the number is that about 7.4% of U.S. divisions saw service in two theatres. This is probably a fairly good estimate, because while higher officers and important specialists (for example Lt. Colonel then Maj. Gen. Jimmy Doolittle) occasionally served in multiple theatres, it was not common for units to be moved outside their division or unit. Service forces and non-divisional troops were also moved around about as much as the divisional troops (assuming they deployed at all), while U.S. Army Air Force personnel probably moved a good bit more.

For the Australian soldiers of the Second Australian Imperial Force, the answer is two.

The Second AIF was Australia's principal expeditionary force during the Second World War and consisted of four infantry divisions, the 6th, 7th, 8th and 9th, and the 1st Armoured division. The 1st Armoured never left Australia, being reserved for the defence of the country in the event of a Japanese invasion.

Of the four infantry divisions, only the 8th served in a single theatre, the Pacific. The 8th took part in the disastrous defence of Singapore and when the island fell, most of the division became POWs.

Of the three remaining divisions, all served in both the North African theatre and the Pacific theatre. The 6th, 7th and 9th divisions were deployed to North Africa, the 6th and 7th from 1940 with the 9th following in 1941.

The 6th and 7th were also deployed to the disastrous Greek and Crete campaigns before being returned to North Africa. In 1942 all three divisions were returned to Australia for service against the advancing Japanese.