Hitler did not fight on any front in WWII, but Nazis fought on
the Eastern front,(Russia) and western front. In WW I Hitler fought
on the western front, but as I remember it he was not a combat vet,
he ran messages.
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Ost - East
Heer -Army
So the word Ostheer stands for the German armies during WWII,
which were fighting on the Eastern front.
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The Italian front was located along the Venetian plane and the
Eastern Alps. This location was used to determine troop setup
during World War I and was changed during WWII.