You have to submit your claim to your insurance first, make a copy of your official receipt. Then after you got the statement from your insurance company, you submit the total amount to your husband's insurance company (with your insurance statement, which shows how much has been paid to you; and the copy of your dental form from your dentist.)
e.g. If you submit $200, and your insurance covers 50%, you will get $100 back. If your husband's insurance covers 100%, you will only get the rest of $100 from his, not $100+$200. In one word, you can get your money back as much as they cover, but not profit from it.