Hi, Kari -
Well, I think this is a good problem to have :)! I appreciate the fact that you're so sensitive to this issue and that you're obviously giving your children's bio Dad a lot of respect in the way that you're handling this.
I think it is absolutely beautiful that your children call your new husband "Dad." Obviously, he's earned it, because, from what I hear, children are more pre-set to RESENT the new partner than to accept them, and especially to bestow such an important title on them.
Growing up, I dated a guy whose father had left his mom and 4 children when they were quite young. She'd eventually remarried a man who had 2 troublesome children of his own, yet he selflessly took care of his own 2 plus the new 4, plus their spouses and children when those kids could not manage themselves properly. He did it all on a very low salary and basically worked himself into the ground to be a good Dad and provider. Eventually, the bio Dad came back into the picture. I was always sorry to hear that guy referred to as Dad because he had not really been the Dad in any sense. The step-dad was called by his name.
Anyway, my feeling is, kids should use the name "Dad" for the person who really does the job! And I don't think there's anything wrong with having two Dads. Maybe you can insert the Dad's name into the reference when you make it, to make things clear - like "Daddy John" and "Daddy Mike" or whatever. My Dad has always had a personal pet peeve about my Mom referring to him to me by his name, and he'll always correct her by saying "Dad."
Considering the respect you express for your children's bio father, I would talk to him directly, in advance, and just let him know that the kids have taken to calling your new husband "Dad" of their own accord. You can tell him you've neither encouraged this nor discouraged this but you're just letting the kids do what they feel. I think that it's very healthy for them to have the freedom to develop these relationships in their own way and that there shouldn't be walls of propriety set up to say that they should hold themselves back from loving their Step-Dad to the degree that he invests in and loves them.
I hope your ex will understand and be supportive of the happiness of his kids in this way. It doesn't diminish him - it just underscores that his children are in a place where they feel a lot of love and comfort, and he should feel very thankful for that.
I hope this helps in some way!
H.