Numbers 12:
From a straight and simple reading of the verse, I think so.
Barnes thought so:1 Miriam and Aaron began to talk against Moses because of his Cushite wife, for he had married a Cushite.
Keil and Delitzsch agreed:The Ethiopian woman whom he had married - (Hebrew, "Cushite," compare Genesis 2:13; Genesis 10:6) It is likely that Zipporah Exodus 2:21 was dead, and that Miriam in consequence expected to have greater influence than ever with Moses. Her disappointment at his second marriage would consequently be very great.
Jamieson-Fausset-Brown disagreed:a short time before, probably after the death of Zipporah, he had contracted a second marriage with a Cushite woman
Pulpit was reasonable:Their irritating disparagement of his wife (who, in all probability, was Zipporah [Ex 2:21], and not a second wife he had recently married) arose from jealousy of the relatives
Some have thought that this Ethiopian woman was none other than the Midianite Zipporah, who might have been called a Cushite in some loose sense by Miriam. The historian, however, would not have repeated in his own name a statement so inaccurate; nor is it at all likely that that marriage would have become a matter of contention after so many years.
Did Moses have a second wife?The natural supposition undoubtedly is that Moses (whether after the death of Zipporah, or during her lifetime, we cannot tell) had taken to himself a second wife of Hamite origin. Where he found her it is useless to conjecture; she may possibly have been one of the "mixed multitude" that went up out of Egypt. It is equally useless to attribute any moral or religious character to this marriage, of which Holy Scripture takes no direct notice, and which was evidently regarded by Moses as a matter of purely private concern to himself. In general we may say that the rulers of Israel attached neither political, social, nor religious significance to their marriages; and that neither law nor custom imposed any restraint upon their choice, so long as they did not ally themselves with the daughters of Canaan (see Exodus 34:16).
From a straight and simple reading of the verse, I think so.