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 ʻalayhi wa sallam, is His slave and Messenger.
We have previously highlighted the prohibition of engaging in an extramarital affair; please refer to fatwa 81356. You should know that engaging in such an illicit relationship while being married is more severe and the sin is graver. Your negative feelings towards your husband and aversion from intimacy with him do not justify committing such a sin. When the wife hates her husband and fears neglecting the due fulfillment of his rights over her, Allaah, The Exalted, made for her a way out in khul’ (divorce at the instance of the wife in return for consideration payable by her). We have previously underlined the ruling on khul’ and some of its governing provisions in fatwa 89039.
You have the choice either to retain your marriage and adhere to patience or to leave your husband honorably and graciously. It is advisable, though, that you should opt for the first and adhere to patience since marriages are not built on love alone, as we explained in fatwa 86796. Please also refer to fatwa 84833.
As for the financial maintenance, it is incumbent on your husband to provide for you; if he is unable to fulfill this obligation and you provided for yourself and for him while intending to be repaid later on when the husband’s financial situation gets better, then you are entitled to ask that you get your money back. However, if you did not intend to take this money back, then you shall be rewarded by Allaah for such an act of kindness and it is an indication of your noble character. For more benefit, please, refer to fatwa 85012.
On the other hand, it is impermissible for your husband to have a relationship with this woman, and the fact that he is inviting her to Islam does not justify it. It is feared that such a relationship would be a means by which Satan lures him into sin with this woman; how could he be inviting her to Islam while he takes her to the casino and the like of the places where prohibitions are committed! Abu Saʻeed AL-Khudri narrated that the Prophet, sallallaahu ʻalayhi wa sallam, said, "The worldly life is sweet and green (alluring) and verily Allaah is going to assign you as vicegerents in it in order to see how you act. So, avoid the allurement of women; verily, the first trial for the people of Israel was caused by women.” [Muslim]
In general, if your husband sincerely wants her to convert to Islam, then he should seek the help of a righteous Muslim woman to invite her or advise her to communicate with an Islamic center, for instance. Thus, he can safeguard himself against fitnah (temptation) and accomplish his objective of inviting her to Islam. For more benefit, please refer to fatwa 88997.
Lastly, if you found out that your husband is having an affair with this woman, then you should advise him and remind him of Allaah and the need to repent to Him of such a sin and end such a relationship. If he listened to you and repented to Allaah, then that is the desired goal; otherwise, it is better for you to leave him. The Hanbali scholar Al-Buhooti asserted, “If the husband neglects any of the rights of Allaah over him, then it is recommended for the wife – just as it is recommended for the husband in a similar situation – to request termination of marriage, i.e. demand khul’, for his neglect of the rights of Allaah.”
Allaah knows best.