How stuck can one be when one has a location:http://www.jewishgen.org/communities/loctown.asp
Čukovac locality 45°09' N 18°59' E E M U G Croatia 150.9 miles ESE of Zagreb 45°48' N 16°0' E
Cukovac populated place 44°36' N 15°27' E E M U G Croatia 87.4 miles SSW of Zagreb 45°48' N 16°0' E
Up to 1918 it was A-H http://users.erols.com/mwhite28/austhung.htm
where 12 different languages were spoken. After the fall of A-H several new countries were formed and one was Yugoslavia http://en.wikipedia.org/wiki/Yugoslavia
The census is correctly having Yugoslavia and you have a location Cukovac which is in Croatia so your research is in Croatia.
You might try the church that Mile and Marta were married in? While you are there, if you want more information request their children's baptismal record. These church records should have a location and parents names.
The 1930 census would have a notation Na-naturalized; Al-alien or Pa-first paper. Follow up on the notation. If your Mike ZIGICH had a social security numbers than his SS-5Form should have a place of birth and parents names.