Quit Claim Deed to add spouse as Co-Owner on Home in New York State

My husband is the sole person listed on the Mortgage, and we reside in NY State. I was told that in New York State, if I don't put my name as co-owner (Joint Tenants) on the home, as in a Deed, that I do not have any ownership rights in our home if something happens. Would the best way to be added as a co-owner, would be to do a Quit Claim Deed? If so, would a Spousal Consent be added to it for me to sign? If so, what is the purpose of the Consent, when we both want to be co-owners? Thank you.