I wish I had some advice, but we haven't told our teenagers anything yet, so I don't have any.
I'm so sorry they found out that way. How did they react?
I can imagine that, same as you, your girls need some time to sort through this. I was a teenager when I found out about my Mom's cheating. Of the many memories from that terrible time, one sticks out - being told "this has nothing to do with you. It's between me and your father." This is very much about the family.
You don't sound like the kind of person who will minimize your girls feelings. Gently reassure them that from day one protecting your family has been the priority. They will see from the steps you've both taken that they are loved.
It might take them a while to sort out their feelings toward their father, so be gentle with them and listen to them as they sort it out. They might not know right now whether they want to talk to their father or whether they need space from him. They might need some time to process the initial shock before they know.
If they do want to talk to their father, could you suggest a family meeting, so all four of you sit down together, if that would make them comfortable? Unless one-on-one seems more appropriate? But it might help to have you present. You don't have to say anything or speak for your husband, but just knowing that one safe parent is there might really help, at least for the first talk.
My experiences (as a child with an unfaithful parent) were somewhat different. The way I found out was coming home to find out that stepmom had moved out and mom was standing in the kitchen with OW. OW and mom told me together. It would have hurt far less if mom and stepmom had told me together, because then at least one safe parent would have been present. Plus, in that case, the affair won.
(((hugs to you and your daughters)))
We told our two older kids (15 and 12) because they knew I was struggling with something and they saw their father at his illest. I do not regret it. They have no idea how it feels for me and the 12 year old is at that pre-teen "everything is about me" stage but that's ok. There are no lies or secrets in my family any more.
"We're not broken, just bent. We can learn to love again."
hugs to you
the kids will be fine
In the meantime continue to be open and honest with your kids. They need to know that you both love them very much, and his choices are just that his choices. He didn't do this because they weren't perfect children and you weren't the perfect wife. This is very important for you help them understand. Then you also need to help them understand that your decisions to stay and attempt to work through it, and forgive him were your choices, and that it had nothing to do with them.
They also need to understand that a wife deserves love and respect, and your H needs to be showing that even more now than ever. If he continues to hide from this it is definitely sending the wrong message to them.
I would lastly consider some family counseling for them and you. If he is an addict there are a lot of skewed family dynamics that accompany that, and it will be helpful for them to understand that. Also make them aware of the characteristics that go with it all, so they can avoid becoming addicted themselves, or becomeing involved with someone who has addictive qualities.