Ban is to strong a word. Paul advises against being "unequally yoked" with a non-Christian, but that is far from banning such marriages.
2 Cor 6:14-18
14 Do not be bound together with unbelievers; for what partnership have righteousness and lawlessness, or what fellowship has light with darkness? 15 Or what harmony has Christ with Belial, or what has a believer in common with an unbeliever? 16 Or what agreement has the temple of God with idols? For we are the temple of the living God; just as God said,
"I will dwell in them and walk among them;
And I will be their God, and they shall be My people.
17 "Therefore, come out from their midst and be separate," says the Lord.
"And do not touch what is unclean;
And I will welcome you.
18 "And I will be a father to you,
And you shall be sons and daughters to Me,"
Says the Lord Almighty.
NAS
1 Cor 7:12-16
12 But to the rest I say, not the Lord, that if any brother has a wife who is an unbeliever, and she consents to live with him, let him not send her away. 13 And a woman who has an unbelieving husband, and he consents to live with her, let her not send her husband away. 14 For the unbelieving husband is sanctified through his wife, and the unbelieving wife is sanctified through her believing husband; for otherwise your children are unclean, but now they are holy. 15 Yet if the unbelieving one leaves, let him leave; the brother or the sister is not under bondage in such cases, but God has called us to peace. 16 For how do you know, O wife, whether you will save your husband? Or how do you know, O husband, whether you will save your wife? NAS