This site is where you need to look.
Indiana Code TITLE 31, Article 14 Table of Contents
As I indicated the law states that your husband has the assumption of paternity and his being listed on the birth certificate means he's the legal father.
Furthermore, an action to change that is supposed to be filed within 2 years. However, since all parties are in agreement, that requirement can be waived.
Bottom line, is you need to get a court to change legal parentage. An adoption may not be necessary, but a paternity hearing with a court approved paternity test will be.