I don't know how long you were married. If you were married long enough you may be entitled to a portion of his pension if you don't remarry. You certainly are entitled to your fair share of everything that was bought or owned while married.
The biggest challenge after filing is setting your course to get an income. SAHM's sacrificed years, or decades of our earning potential, expecting to spend forever with one person. When that plan becomes a fractured fairytale, we need to sort how to make up for years of missed income when we retire. Our highest 35 years of income are what Social Security base our checks off of when you retire.
Right now focus on the path ahead, but keep that tidbit of information in the back of your mind. He benefitted from you raising children. Now it's time to sort out the non romantic part of a relationship, the divorce.
He may be required to move or you both may stay put. You will likely get joint custody or full custody if he wants no part of the responsibility. Be prepared for both. He may opt for paying child support so he can have a career. Depending on the ages of your children he may have a number of years of child support to pay, but it's no walk in the park. If you get custody, you have to juggle a job, sick kids, vacations from school, child care, and a million things he won't have to deal with.
Men often take the easy way out, pay child support, spend a few hours here and there and call it "parenting". The real heroes are the ones that get up tired, go to work sick, fix meals, do homework, go to school functions, buy groceries, and do laundry all while being the solo parent other than child support.
The peace of mind of not dealing with infidelity is worth the divorce. You will know where you stand, and can plan accordinly. It won't be a walk in the park, but it will fall into place at some point. Chances are if you suspect he's having an affair he most likely is.
Find out with a free consultation what to focus on, and gather financials. Do as much of the work yourself as you can, and try to remove emotion as much as possible when making life decisions. Don't make them with your heart, make them with your head as a financial plan for YOU as the focus. Let him worry about himself. Don't get caught in a mind game trap of considering his wants or needs above your own. Divorce is messy, but it's a business arrangement that you need to fight and advocate for yourself in.
I hope you find peace in this, but it will drain you. If you have family or friends lean on them while you make decisions.