Thing are probably different for a therapist but I used to work in a medical office. Whenever we received a request for records to be sent to another office, we never included the physician notes. The History & Physical, test results or reports, x-rays, consults, assesments, medications and treatments, and physician orders. But as far as the general notes, those belonged specifically to the clinic or office. The only exceptions were if there was something specific that was noted by the physician and was necessary in care of that patient, but that was very rare.
As far as his parental rights go, though he is entitled to receive a copy of the medical records and I would assume that this would include therapy, I’m not sure if the therapist would be required to disclose confidential information with a parent if the child requested that they keep it in confidence. The therapist may be able to generalize by saying something along the lines of what the daughter is having issues with and what she believes that your husband could do to help her through some of these issues.
My youngest stepson went through some counseling during my husband and his ex separating and divorcing. The therapist did speak to both of them about his issues, but I do not believe that everything was disclosed. You may try setting up an appointment to discuss her progress and ask what is needed to request a copy of the records. If the office tells you that he can not request a copy you can ask if a subpeona is necessary. Try the non confrontational approach first and see how far it gets. He will most likely have to sign a request for copies but that may be all it takes.