If you and your husband are on the bill for the phone company you can request a record of all SMS messages and calls from them. If you want to search his phone legally you would need a warrant. As if you do something illegal you might end up on the loosing end if you go to divorce court.
If it was just sex, try to realize that monogamy is a social construct.
You do know what a social construct is, right?
Oh, never mind.
If a private investigator does find something then you have all legal documents to use, with a hacker you would have nothing that you could legally use if you chose to get a divorce because you obtained evidence illegally. Then your husband would have a legal standing to divorce you and get the bulk of what ever you two had together after getting married. Which would grant him with the ability to sue you afterwords in criminal and civil court using the evidence you obtained illegally against you.
It is a loose loose situation for you if you obtain what you want to know illegally. You can only find out what you are wanting to know illegally by getting a private investigator to legally obtain what you asking for. When they are done they will normally present you with their findings with high quality images, videos and other documents that you can have when the investigation is done to do with as you want.
In short, a hacker is illegal to use and a private investigator is the route you should take to keep things private so no one knows what is going on but you and the private investigator.
but honestly this isn't a good idea: its about a 95% chance that any hacker that you find that agrees to work for you will either 1) steal your money and not give you what you want and also possibly hack into your bank account and steal ALL of your assets, or 2) be an FBI agent in disguise and arrest your for cyber terrorism or some such.
long story short: don't hire a hacker.