You should consult with your attorney. He/she can advise you whether it was appropriate for your Husband's attorney to give him these materials. In all likelihood, it was appropriate.
I do no domestic work, and so you should treat my thoughts as general information. The process of "discovery" in any kind of civil lawsuit in Ohio generally does not limit what is done with information provided by the parties, unless there is a special type of court order (called a "protective order") which allows parties to designate information as confidential and agree how such information will be handled. It might be possible to retroactively get agreement on such restrictions, but if things are hostile it seems unlikely. All that said, if any abuses occur you should make sure your lawyer is fully informed, and she might be able to get the court to intervene--or at least poison the well against your ex. Good luck, and remember that you should not hestitate to ask your lawyer any questions you have--she will welcome your involvement.