I'm more than sure that OP knows/understands the severity of her current situation. The bottom has just dropped from her world. Her husband has been arrested. He has admitted to a online relationship and a subsequent meeting of a 15YO girl. The word RELATIONSHIP jumped out at me because you are talking about a length of time. Not a "we chatted last night and decided to meet for coffee and a chat" sort of scenario...
If/When he is charged, depending on the severity? (Honestly, I don't think there is an if) There will be a strategy meeting with professionals to decide how to proceed. There will be social services involvement there are no, if's, but's or maybes about it.
I know of a woman who worked in a prison. She ended up having a relationship with one of the inmates. She lost her job. On his release they started where they'd left off. He was serving time for a brutal rape on one of his friends mother. Long story short. They had children together, he isn't allowed EVER to be alone with the children. There will always be involvement from other agencies to safeguard those children. Their father will ALWAYS be on a sex offenders register. She made her choices, but, the children that followed had none.
Please don't buy into his explanation OP, because the is no plausible one. Whatever you need to know, do it through either SS or another agency. Like others have rightly suggested get yourself a solicitor. Go to your local CAB office and see if you meet the criteria for free legal aid?
Be kind to yourself. YOU didn't do this.