Will the state of New Hampshire allow my spouse (not married) to adopt my daughter?

I'm filing a petition to terminate the parental rights of my daughter's biological father. I ended the relationship w/ bio very early in pregnancy due to an unhealthy relationship. And moved to Nh where I began a relationship with a childhood friend. We have been together for 5 1/2 years and had two more girls. He considers my first born his, and they have an unbelievable bond. She is his first born and daddy's little princess. He wants to legally adopt so we can get a new birth certificate and hopefully delay any questions should they ever arise. Bio has never met her, and continues to expresses he wants no part in her life for a number of different excuses, and doesn't want to pay child support for her. I'm confident his rights will be terminated, but nervous the courts won't let my boyfriend adopt my daughter because we are not married. If they won't allow it because we aren't married could bio sign his rights over to him?