There were some armored units in addition to the air support. The communists supplied entire Divisions of troops.
Italy supplied a lot of ground troops to assist Franco as well; I just don’t seeing the war being gradually morphed into a Nazi invasion of Spain with Franco as their puppet. Both the Nazis and the USSR provided weapons and specialists, while the ground war was fought primarily between Spaniards; Italy provided troops for Franco, while global communism provided troops for the communist government.