If, as some believe, Miriam and Aaron spoke about Moses and Tzipporah, what need was there for the Torah to describe Moses’ wife as אשה כושית when everyone is well aware that Moses married Tzipporah the daughter of Yitro who was a Midianite, not a Cushite. Tzipporah could not have been described as Cushite seeing that the Cushites are descended from Cham, and the Midianites are descendents of the sons of Keturah, Avraham’s concubine, who bore 6 sons for him one of them being Midian. [Rash’bam’s argument is tenuous, for if Keturah was the same person as Hagar, according to most commentators, seeing that Hagar was an Egyptian, a woman descended from her could be described as Cushite, seeing that Mitzrayim, Egypt, was a descendant of Cham, also. Ed.]
Josephus Antiquities
252 Tharbis was the daughter of the king of the Ethiopians. Observing Moses leading his army near the walls and fighting courageously, marveling at the inventiveness of his undertakings and believing that for the Egyptians who had earlier despaired of their freedom he was responsible for their success, while for the Ethiopians who had prided themselves on their successes against them, he was responsible for their danger in the extreme, she fell madly in love with him. When passion got the better of her, she sent to him the most trustworthy of her servants to enter into discussion about marriage.
253 When he accepted the proposal on condition of her surrendering the city and gave pledges on oath, indeed, that he would take her as a wife and that, having conquered the city, he would not transgress the agreement, the deed anticipated the words. After the annihilation of the Ethiopians, giving thanks to God, Moses contracted the marriage and led the Egyptians back to their land.