The Bible rarely mentions a man's marital status. We are sometimes told plenty of details about individuals and events in which they were involved, only to remain unaware of whether they were married. Occasionally we come across a single statement at the end of the Biblical account which gives us a clue to the answer, such as that of Gideon.
"And Gideon had threescore and ten sons of his body begotten: for he had many wives. And his concubine that was in Shechem, she also bare him a son, whose name he called Abimelech." Judges 8 vv 30-31
Put simply, the Bible doesn't often consider it important to tell us whether a man was married, and if he was, to how many women he was married. This has led to many men being claimed as "monogamist", because only one wife is recorded, or because the Bible doesn't specifically pick them out as polygamists.
It has often been noted that the example of many godly men in the Bible who were polygamists is, to say the least, a little inconvenient for those who claim that the Bible preaches monogamy. The polygamists definitely have Abraham, Jacob, David and Solomon as their predecessors. The monogamy-only crowd can only argue from silence or from limited records, and they don't really like it. Hence it becomes very important to claim major Bible characters as monogamous, if only to try to counterbalance the blatant polygamy of so many of God's finest. And if you are looking for great Bible characters then Moses is certainly up there with the best of them. The man who wrote the five books of the Torah, who first recorded that marriage made a man and his wife "one flesh", who first gave the law to the people of God, is an impressive person to have on your side of the argument. In fact, if he turned out to be a polygamist this would make life difficult for those who suggest that his writings contain material incompatible with polygamy. And as a bonus to those obsessed with monogamy, we only know the name of one wife of Moses!
For these reasons Moses is sometimes claimed to be monogamous, and those of us who dare to suggest otherwise are often "put right" in no uncertain terms by those who make those claims, usually with some sort of side-swipe to suggest that this proves we do not know our Bibles very well. Moses they say, was married to Zipporah, and no other wife is recorded, and so we ought not to defame him by claiming he was engaged in such a notorious practice as polygamy.
So what do we know about Zipporah? Well we know she was a Midianite and that Midian was the son of Keturah, one of Abraham's wives, and that she was brought back to Moses by her father, as soon as Moses had led the children of Israel out of Egypt. We then find that Aaron and Miriam complain about a wife of Moses in Numbers 12. The Bible says that Aaron and Miriam spoke against Moses "because of the Ethiopian woman he had married." - or if you are old-fashioned like me, because of his 'Cushite' wife (as Cush is how the word was translated before the translators began using "Ethiopia". In fact it may be more accurate to use the term "Sudan").
The question is - "Is Moses Ethiopian wife of Numbers 12 the same as Zipporah, his Midianite wife?"
Well, Zipporah was descended from Midian, and therefore Abraham and ultimately from Noah's son Shem (Gen. 25 vv 1-4). Cush, however was descended from Noah's son Ham, not Shem (1 Chr. 1 vv 8-10). So the titles of Cushite (Ethiopian) and Midianite refer to entirely different nations from different descendants of Noah, and it may be considered unlikely that Zipporah descended from both Cush and Midian, because of the tradition of endogamy mentioned in the Bible, where people married their own kind, and normally went to some trouble to do so.
Some have suggested that Zipporah was "an Ethiopian subject" - because it is clear that, as a Midianite, she was not an ethnic Ethiopian. But where does the Bible say this? Nowhere. In fact, does it talk of anyone in such terms - did the Jews become Babylonians when they were in the captivity? No. Were they called Egyptians when they were in Egypt? No. The idea of some being called after a certain nation because they were subject to that nation does not appear to be found in scripture. And, in any event, it is clear that Zipporah is in no way subject to Ethiopia - she is married to the man leading Israel. It is hard to imagine how she could be less subject to any other nation.
Also, there is no scriptural evidence that the Midianites were subject to Ethiopia, and no separate historical evidence has been provided. Take a look at a Bible atlas - they are not even close - Cush (Ethiopia) is to the South of Egypt - To get to Midian from Egypt you go East across the Gulf of Suez, East across Sinai, East across the Gulf of Aqaba and, congratulations, you have arrived. It is not a very credible suggestion that Cush ruled Midian, and that because of this Midianites were called Cushites.
The explanation then begins to look a bit contrived - as if trying to get round a difficulty. The Bible is happy to talk of Zipporah as a Midianite. Her name and ethnic origin are not hidden - we even know the name of her brother (Numbers 10 v 29) and the name of her father (Reuel in Exodus 2v18 and Numbers 10 v29) and of Jethro, another male relation, in Exodus 3 v 1. The point is that she is not Mrs. Anonymous, and there is no reason for skirting round her identity. But suddenly in Numbers 12 we are talking of "the Ethiopian woman he had married" - no name or details other than that she is a Cushite (Ethiopian).
And this is strange, because only two chapters earlier (Numbers 10v29), Zipporah's family are being referred to as Midianites. Midianite is the term that Numbers used for her people - so when it uses Cushite, there is every reason to suspect that it is referring to someone else.
To believe that this woman is Zipporah is to believe that God happily referred to these people as Midianites, then called them Cushites in Numbers 12, and then went back to calling them Midianites, that he was happy to call Zipporah by name, and then changed his mind in Chapter 12 and instead called her something she had never been called before, relating her to a nation that she didn't come from but that she might, just might, have been subject to, although there is no evidence or reason to believe that is the case.
A little far-fetched?
So what is the deal with Moses and the Cushite wife?
Well, there are two things. Firstly we know that Moses was married to Zipporah, and that he is married to this Cushite. If you check the first verses of Exodus 16, 18 and 19 you will see that Zipporah returned to Moses sometime in the second or third month after the exodus from Egypt. If you check Numbers 10 vv 11 and 29 you will find that one year later her Father is still Moses Father-in-law (i.e. Zipporah is still with us) and if you follow the action into Numbers 12 you will see that hardly any time passes before Aaron and Miriam get all hot and bothered about the Cushite wife. There is very little time available for Zipporah conveniently to die in order to maintain Moses as a monogamist.
This means essentially, that it appears that Moses was still married to Zipporah when he was married to the Cushite, i.e. Moses didn't just remarry when she died - Moses was a polygamist.
Secondly, the one thing we know of this other wife is that she is a Cushite, a descendant of Ham. What do we know of the Cushites? That Jeremiah 13 v 23 records a prophecy asking, "Can the Ethiopian change his skin, or the leopard its spots?", that Cush means "black" or "burnt face" and these nations populated Africa, which is still where you will find Ethiopia. In other words, Moses married a black woman as well as Zipporah, and his family didn't like it.
So it seems that Aaron and Miriam didn't like the Cushite - possibly because she was black, or possibly because it made Moses polygamous, or possibly because of both reasons - and God punished them for it. Ironically, Miriam's punishment turns her white as snow, which may be another clue to the nature of the dispute.