Wa `alaykum as-salam 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.
Sister, first of all, we are impressed by your question, which emanates from a thoughtful heart. May Almighty Allah help us all adhere to the principles of this true religion, Islam, and enable us to be among the dwellers of Paradise in the Hereafter.
No doubt, adultery is an abominable and heinous sin in Islam. It violates peoples’ honors and destroys families and may lead its doer to Hell in the Hereafter and great loss in this worldly life. It is unbecoming of a Muslim husband to leave what is halal (Arabic for: allowed according to Islamic teachings) and go for haram (Arabic for: prohibited according to Islamic teachings) or leave what is pure and go for the impure and filthy. Any Muslim involved in this heinous sin is required to fear Allah and sincerely repent to Him before it is too late.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
If you have clear evidence that your husband has been committing adultery and he has not changed his behavior and therefore you are unable to trust him, then that is a valid ground for you to get a divorce from him.
As Almighty Allah tells us in the Qur’an, “The adulterer will not marry save an adulteress or an idolatress. And for the adulteress, none will marry her except an adulterer or an idolater. All that is forbidden to the believers.” (An-Nur 24:3)
The only exception to the above rule is when the person has sincerely repented and has changed and made amends to redeem himself or herself; in which case, you are allowed to continue the marriage.
May Allah inspire us to love all that is good and pure and make us abhor all that is filthy and obscene.
Allah Almighty knows best.
Excerpted with slight modifications from Islam.ca