I should think that this would be explicitly covered in the divorce decree, and if not, your husband should go back to court and get it clarified.
Personally, I would think that as a parent, the question is not just what he has to do under the law, but what he should want to do for his daughter, since his interest in this little girls welfair did not end with the demise of the relationship with her mother. I am sure that there is a degree of what is equitable distribution of responsiblity for this child, but, the primary desire for any parent is to see to it that the child has all the care they need, even if they have to pay more than thier fare share for that child to get it.
In any case, that it is not clear to your husband, means that it is not clear to the child's mother eihter, and they need a riliable court document that does not leave room for interpretation so that everyone is on the same page.
M.