As-Salamu `alaikum,
I am married to a non-Muslim woman in the UK in a register office and we’re now expecting a baby. She was a Christian who used to go to church but stopped because she said priests do things that they ask others not to do. As a result, she said she lost her belief and no longer belief in God. I knew this even before the marriage but did not know that I can’t marry her because she no longer belief in God. She agreed that any children we have will all be Muslims and does not object to convert to Islam when she finds her belief. She reads books about Islam and visits websites in order to know more about the religion.
What does the Quran says about this?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

If what you mentioned is true that this woman had no belief in the existence of Allaah at the time you got married to her, then you have married her while she was an atheist and not from the People of the Book, which means that your marriage to her is invalid, since it is impermissible to marry a disbeliever unless she is a chaste woman from the People of the Book. Allaah The Almighty Said (what means): {And do not marry polytheistic women until they believe.}[Quran 2:221] Please see Fatwa 88451.

Thus, it becomes incumbent upon you to leave her, and it is unlawful for you to have intimacy with her. As for the baby, he is attributed to you if you thought (when you married her) that your marriage to that woman was lawful. Shaykh Al-Islam Ibn Taymiyyah said: "All Muslims are agreed upon the fact that any marriage thought by the husband to be valid, in which he has sexual intercourse (with his wife), requires that his child be traced back to him, and both inherit from each other, according to the consensus of the Muslims.”

On the other hand, it should be clarified to this woman the real nature of Islam as being the religion of all the Prophets. In this connection, you may benefit of the relevant articles and Fataawa in our website. For more information, refer to Fataawa 81979, 86091 and 88906.

However, if this woman embraces Islam, then, it becomes permissible for you to marry her with a new contract according to the conditions of Islamic marriage. For information about the conditions of marriage, see Fatwa 83629.

Finally, we draw your attention to these two points:

First: what is called civil marriage most often occurs without a guardian; and marriage without a guardian is invalid according to the preponderant opinion of the Muslim scholars. So, the Muslims should beware of that, and be keen on establishing their marriage according to the Sharee‘ah (Islamic law).

Second: Marriage to a non-Muslim woman (i.e. a woman from among the People of the Book) has many disadvantages to the religion of the man and his offspring after him. So, Muslims should not seek it, particularly in our time. For further benefit, see Fataawa 88451 and 84724.