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 is His slave and Messenger.
You did not clarify to us what you mean by your husband cheating you, as some people may mean by this the marriage of a husband with a second wife, although there is nothing wrong Islamically with this. This term can also be used for a husband establishing an affectionate relationship with a non-Mahram (marriageable) woman, and this is forbidden as we clarified in Fatwa 81356.
Therefore, if what you meant is your husband establishing a forbidden relationship, and you are certain that he did this, then you should advise him in a soft and gentle manner and remind him of Allaah The Almighty as he might repent. If we presume that he persists in doing so and you are harmed by staying with him, then it becomes permissible for you to ask him for divorce or Khul’ (divorce initiated by a woman). However, you should not hasten to do so as the preponderant [greater] benefit could be in being patient with him and trying to rectify him.
Of course, this is if you are sure that he did this. However, if you are just suspecting this, then this is forbidden. In principle, a Muslim is innocent and it is not permissible to spy on him or investigate about his matters; Allaah The Almighty Says (what means): {O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin. And do not spy or backbite each other. Would one of you like to eat the flesh of his brother when dead? You would detest it. And fear Allaah; indeed, Allaah is Accepting of repentance and Merciful.} [Quran 49:12]
In addition to this, by spying on him and investigating about him, you make yourself sorrowful and unhappy, and you may believe him if he tells lies to you and you may not believe him if he tells you the truth. Thus, it is wise not to spy on him and investigate about him.
Finally, we advise you to beware of Satan and his plots and endeavors in separating spouses. Jaabir narrated that the Prophet said: “Indeed, Iblees (Satan) places his throne upon water; he then sends detachments [for creating dissension]; the nearer to him in rank are those who are most notorious in creating dissension. One of them comes and says: 'I did such and such'. And he says: 'You have done nothing'. Then one amongst them comes and says: 'I did not spare so and so until I sowed the seeds of discord between him and his wife'. Satan goes near him and says: ‘You have done well!’” [Muslim]
Allaah Knows best.