I currently am in the midst of a divorce and my estranged husband is telling me that my name on the deed is meaningless and that I am not half owner. The mortgage is exclusively in his name but am I still entitled to half of the house upon settlement?
You husband is wrong.

The best way to explain the situation is like this:
Right now the asset has three owners: you, him and the bank as a lien holder. Let's say you sell the house today and pay the principal to the bank. The bank and the mortgage disappears leaving you two as joint owners of a chunk of money that's left (I am assuming there is a positive equity).

Depending on your state laws, there could be a lot of legal maneuvering. One side may try to prove that the money is his because he was the one making payments or that the money should be yours because you painted the walls and chose fixtures that allowed the house to sell at a higher price. But, the cut and dry arrangement is usually 50/50; anything else would be unusual.

If the house is underwater (the amount owed is larger than the value), you have an upper hand because you are not on the hook for any liabilities. Just let him have the house and the mortgage with it.
Yep..if your name is on the deed, you own half, regardless of who's name the mortgage is in. The mortgage just tells the bank who is liable for repayment of a loan and has nothing to do with ownership. Your soon-to-be-ex cannot do anything with the property without your agreement.
You husband is wrong!!! You own 1/2 of the property and he can not see it without you. The best part of this is he is responsible for payment and you are not, because the loan is in his name and not yours. Ownership comes from chain of title and you will show up a 1/2 owner. He's SOL.
More accurately, you are likely a co-owner, either as joint tenants in common or joint tenants with right of survivorship. But yes, you have an ownership interest; that is determined by the property title, not the mortgage loan.
Good thing it's not up to him - it's up to the judge - ha ha for him he isn't in charge of everything in this world!

Yes you're 50% owner. Depending on the deed, these things go a bit differently i.e. joint tenancy.
yes you are half owner. he will not be able to sell the home without your approval. you will need to sign the deed if he ever sells.

the fact that mortgage is in his name is tough luck for him.
Your name on the deed in effect allows you the same rights of ownership that he has. He is full of ****. Just trying to be intimidating to get you to sign a quit claim deed. DON'T DO IT.