In Islam the burden of proof for accusing another of having sexual relations is very high and for a good reason. It is a very big sin for which the penal code is applied. Those Muslim who are living in the west and somehow fall into this sin, should, in my opinion, seek forgiveness from Allah and not tell anyone - especially their spouse. Now that you know, it is your choice to remain in the marriage or leave. If, in my opinion, your marriage, prior to knowledge of this occurrence was great - you love your husband, then you may want to consider whether to forgive, and move on, or not. Allah has allowed divorce for a reason and you have every right to take this option. Your husband made a bad mistake, and may very well become a better person given your understanding and support. Think deeply about your ability to forgive and move on. Are you able to live with this severe blow to trust in your relationship? Certainly you are now sad and depressed, this is normal, but in time the pain will likely lessen. It will not be easy. Only time will heal your hurt feelings. We ask Allah, Most High, to guide you to the best decision. Laws regarding him leaving would depend upon where you live and safety issues.
"To Allah we belong and unto Him is our return. Oh Allah! recompense me for my affliction and replace it for me with something better." Insha'Allah, whoever says this supplication Allah will replace for him with something better..Muslim
عن ام سلمه رضي الله عنها قالت : سمعت رسول الله صلى الله عليه وسلم يقول : « ما من عبد تصيبه مصيبة ، فيقول : إنا لله وإنا إليه راجعون : اللهم أجرني في مصيبتي ، واخلف لي خيرا منها، إلا أجره الله تعالى في مصيبته وأخلف له خيرا منها . قالت : فلما توفي أبو سلمة ، قلت كما أمرني رسول الله صلى الله عليه وسلم فأخلف الله لي خيرا منه رسول الله صلى الله عليه وسلم . رواه مسلم