In the Old Testament when a man from one tribe married a woman from another tribe, what tribe would they be considered from? For example: A man from the tribe of Judah married a woman from the tribe of Levi and had children what tribe would that family be considered from?
The tribe is based on the husband's tribe. You can see this is the various genealogies in Bible. The male lineage is always traced to head of the tribe. "But Zelophehad the son of Hepher, the son of Gilead, the son of Machir, the son of Manasseh, had no sons, but only daughters" (Joshua 17:3).
"So the inheritance of the children of Israel shall not change hands from tribe to tribe, for every one of the children of Israel shall keep the inheritance of the tribe of his fathers" (Numbers 36:7).
Zelophehad had only daughters, so when he died, his daughters inherited his land. A concern arose that if these daughters married into another tribe, their tribe would lose control of some of their allotted land. The solution was that women who inherited land were restricted to only marry men of their own tribe.
"And every daughter who possesses an inheritance in any tribe of the children of Israel shall be the wife of one of the family of her father's tribe, so that the children of Israel each may possess the inheritance of his fathers. Thus no inheritance shall change hands from one tribe to another, but every tribe of the children of Israel shall keep its own inheritance" (Numbers 36:8-9).