Husband cheating having affair and when caught he...

In the event that you reside in the UAE, the applicable law is the Personal Status Law, and therefore several legal measures can be taken to file a criminal complaint against the husband and the other person on charges of improving disobedience, which means spoiling the marital bond and stipulated in the Federal Penal Code in Article (312)
Article (312)
Detention and a fine, or one of these two penalties shall be imposed upon any one who commits any of the following crimes:
1. Abuse of any sacred or holy Islamic rites.
2. Blaspheming any of the divine recognized religions.
3. Condoning or encouraging sin, publicizing it, or acting in a manner that tempts others to commit such sins.
4. Knowingly eating pork by Muslims.
If any of such crimes is committed publicly, the penalty shall be detention for at least one year, or a fine.
Moreover, you can file a divorce case for the damage that followed you by going to the Family Support as article 16 states,
1. The lawsuit concerning personal status matters shall not be admitted before the court unless it has previously been submitted to the Family Orientation Committee. Are excepted from this provision, matters concerning wills, inheritance and like matters, summary and provisional lawsuits concerning alimony, fostering, guardianship as well as cases that cannot be settled by conciliation such as evidence of marriage or divorce.
2. Where conciliation between the parties takes place before the Family Orientation Committee, it shall be recorded in a minutes signed by the parties and the competent member of the Committee. The minutes shall be sanctioned by the competent judge, enforced as an executory deed and shall not be subject to any means of appeal except if it is in violation to the provisions of this Law.
3. The Minister of Justice, Islamic Affairs and Wakfs shall issue the implementing regulation organizing the work of the Family Orientation Committee.
If one of the parties demands the divorce, the consultant shall submit a letter to allow that party to file a case of divorce at the court.
The letter may be submitted to the court at any time within 30 months. The procedures of divorce are based on the estimate authority of the court as each part shall provide the evidences to defend.

Yes, the complaint must be submitted for the purposes of conducting an investigation and initiating a criminal case, according to the text of Article (10) of the Federal Penal Procedures Law.