...My servant Moses. He is faithful in all my house.
Numbers 12:7 ESV

Moses' sister Miriam was angry at him because he married a Cushite woman. There is some disagreement about whether this is another name for Zipporah (a Midianite, not a Cushite) or if this is a second wife. Personally, I find the arguments for "Cushite woman" in v1 being Zipporah to be weak at best. I think it's much more likely to be a second wife that he married during the Exodus since he had sent Zipporah to be with her father before he went to confront Pharaoh.

Miriam is angry because he married a Cushite--a black woman--not because he married a second wife. There is no hint in the text that a second wife is an issue with anyone involved. God even rebukes Miriam, saying that Moses "is faithful in all his house", as opposed to Miriam and Aaron who were mad that Moses had married a black woman.