I NEED ADVICE PLEASE HELP ME!!!!!!!!

recently I found out my husband of 13 years (hes 36; and im 38) has been engaging in an affair with his secretary who is at college studying medicine.. and doing part time work to pay her bills. I got a call from someone who knew about this affiar and that they were both at her house engaging in intercourse .when I went around there she was in a see through nightie and he was just walking out the door hugging her with a big smile on his face... our two beautiful children 6 &7 were out in the car listening to the hole ordeal. I left in a huff... then I later returned to see this women who turned out to be 20 years old she spoke to me and told me she had no idea that he was married and no idea he had children. she told me everything about him and her over the past year... she new EVERYTHING about him... and his family. as though she was a fly on the wall.. after returning home he denied the hole thing ever happened should i beleive the man i love? and keep a happy family or give up on him?? is he lying or not? he kept denying her and said she was obsessed with him and she was crazy... ive kicked him out but he still comes and see's our children... what should i do? let the man i love (who cheated on me) back into our home? and around my children.. we were such a happy family why did he do this??