There are two parts to this question:
I seem to remember an account in the scriptures where YHWH gives one of his own to marriage with a nonbeliever. Is there such an account?
Secondly, what is the biblical defence for marriage to be between two believers only? Is there a possible contrast when one understands from the New Testament that God does not distinguish between people? (See Acts 10:34).
The incident of God commanding a Godly man to marry a not so Godly woman is in Hosea 1:2-3.
The beginning of the word of the LORD by Hosea. And the LORD said to Hosea, Go, take unto thee a wife of whoredoms and children of whoredoms: for the land hath committed great whoredom, departing from the LORD. So he went and took Gomer the daughter of Diblaim; which conceived, and bare him a son.
The idea is of a Godly prophet marrying, as to sanctifying, her unto salvation. Yet still, Diblaim was Jewish in the northern kingdom.
Here is one view.
This narrative teaches that Hosea was emotionally attached to Gomer and felt obligated to her. God tried him when He told him to part from her and her children, but He did not intend this order to be fulfilled. Rather, Hosea was to learn from the husband and wife relationship the emotions of love, compassion and commitment that a prophet must feel for his people. https://jwa.org/encyclopedia/article/gomer-daughter-of-diblaim-midrash-and-aggadah
On the second part of your question, the marriage idea is to live in peace.
1 Cor. 7:15 But if the unbelieving depart, let him depart. A brother or a sister is not under bondage in such cases: but God hath called us to peace.
Peace is tranquility, harmony, no fear, salvation.
1 Cor. 7:14 For God is not the author of confusion, but of peace, as in all churches of the saints.
So, if a believer is married to a non-believer, peace may be hard to come by.
