Interracial marriage per se is not forbidden in Scripture. It’s true that the Israelites were strictly forbidden to marry people from other racial or ethnic groups, as we read for instance in Deuteronomy 7:
When the Lord your God brings you into the land that you are entering to take possession of it, and clears away many nations before you, the Hittites, the Girgashites, the Amorites…etc., and when the Lord your God gives them over to you, and you defeat them… You shall make no covenant with them… You shall not intermarry with them, giving your daughters to their sons or taking their daughters for your sons…” (Deut. 7:1-3)God strictly prohibited his people from marrying outside of Israel—marrying people of other racial or ethnic backgrounds. But the command was not grounded so much upon race but upon faith. That is to say, God was not concerned with racial purity but with religious purity. The people of Israel were forbidden to marry outside the faith, which at that time happened to be largely confined to their own race. They were not to marry someone who was not a worshipper of the one true God and incorporated into the covenant community of Israel.
Now if someone was from a foreign nation, and a worshipper of a pagan deity, but came to believe in the one true God, the God of Israel, and was formally incorporated into Israel, then he or she was permitted to marry an Israelite.
We have an example of this in Rahab, the harlot from Jericho, who was converted from paganism and became a worshipper of Jehovah. (See her confession of faith in the God of Israel at Josh. 2:11.) And because she was converted, she was eligible to be married to an Israelite, notwithstanding the fact that she was not herself an Israelite by birth. In fact, we discover that she did indeed marry an Israelite—a man named Salmon—and as a result of that union and the children that she gave birth to, she became an ancestor of Jesus Christ (Matt. 1:5).
We have other Biblical examples as well, the most well known perhaps being Ruth, a Moabite, who converted and eventually married a godly Israelite named Boaz, and she also became an ancestor of Christ (Matt. 1:5).
Moses also married a non-Israelite, since it is said he married a “Cushite woman” (Num. 12:1). “Cushite” was the ancient term for Ethiopian, so that Moses apparently married a black woman. She was likely one of the mixed multitude that came out of Egypt with Israel (Ex. 12:38), and although coming from a pagan background she had become a worshipper of the true God.
In all of these examples we see that faith takes precedence over ethnicity. Or to say it another way, the issue is not race but grace.
I should add that the issue is just the same for Christians today. Believers are not prohibited from marrying someone of a different race, but they are prohibited from marrying someone of a different faith (or of no faith at all). I must stress this: Christians are not to marry non-Christians. They are not to marry people who unfaithful to the Lord. This is a command of God. In 1 Corinthians 7:39 Paul says that Christians are to marry “only in the Lord,” meaning they are to marry only another faithful Christian. In 2 Corinthians 6:14 he says that we are not to be unequally yoked with unbelievers.
But if a man and a woman are both faithful Christians, it doesn’t matter what their respective races might be. It doesn’t matter, that is, in the eyes of God. And it shouldn’t matter to us either. After all, we are all descended from one man. God “made from one man every nation of mankind to live on all the face of the earth” (Acts 17:26).