There are so many verses that could take you one way or another... Bit what I would say is; Pray without ceasing. Do not allow your mind to go down the road of worst case scenarios. Talk to God when you would be idly thinking about the situation. In everything remember the Lord. I do not believe that anyone here can give you true advise whether to stay with, or leave your husband without hearing something from God for you, and I would be utterly weary of anyone giving such advise without being intimately aware of your situation, coupled with much prayer.
But I believe most of all that he is your husband, and it is up to God to realize whether or not he remains as your husband.
I only say this as a child of 4, with no experience other than one who watched his father deal with an adulterous mother, and how he responded in the Lord.
But above all else, remember the Lord for your childrens sake. The one thing I love my earthly father for more than anything else; Is no matter how painful it was, he always put the Lord first in all he did for us. And for that I am the Christian I am today, and owe him more than I can ever say on a screen.
My prayers are with you and your children. Much love and God bless.