Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
The husband should first take all the possible steps he can to return his wife to Islam. He should approach her softly trying to remove her misconceptions about Islam. He can seek help from specialized persons and websites.
Responding to your question, Dr. Salah Al-Sawy, the President of the Sharia Academy and the Secretary General for the Assembly of Muslim Jurists in America, stated,
Allah Almighty said, “And do not maintain marriage ties with the polytheists.” (Al-Baqarah 2:221)
If the wife renounced Islam and there is no hope of her coming back, then this woman becomes unlawful for this brother. She cannot be in a marriage tie with a Muslim. A Muslim is permitted to get married to Muslim, Christian or Jewish women only.
However, we advise this brother to show compassion in talking to her. He should work hard to remove all her misconceptions and draw her closer to Islam. If he is unable to get her back to Islam, he should divorce her and Allah will replace him with a better one, for whoever leaves something for Allah’s sake, Allah will compensate him with a better one.
Allah Almighty knows best.