Hi OP,
I can see that you have asked a question and people have then made assumptions as to why the mother is refusing access you have then answered some generalised statements on when you think dads should be excluded/have supervised visits and people assume your DH used to beat his ex-wife... Wow that's a lot of negative assumption you, you poor thing.
Now I'm going to go on your post and comments to which it sounds like you have been in a relationship for 6 years married for 4, your partner before that was a "good" dad and he split up from their mother and he has then paid maintenance as any absent parent should and would like to see his children but the mother stops this.
You asked for an opinion and in my opinion it is very very wrong for a parent to stop the other parent having any contact if the children want to see the other parent and the other parent will not cause harm to the children. Regardless of how vile the parent thinks the other one is :)
What can you do? Well you can only go through the court, having been through 18mts of a court case (my situation is opposite Dad has full custody, mother doesn't ever turn up for visits, cancels last minute as something better comes up) I know it's very very tough and this doesn't sound fair in the children
Unfortunately dads have no rights until it goes to court but her not allowing access will not look good in the court. Your husband needs a good lawyer he needs to see is kids regularly (get lawyers to talk to lawyers) and stick to it to start a pattern and he needs to fight for them. I'm guessing he has already gone through the mediation stage? You have to do that now I think
Wish you much luck - and is suggest giving more facts to begin with otherwise your end up defending yourself as lots of people automatically side with the mother without all the facts.