my rights as the mom as well as his rights

When you are not married and you have a child, you would need to file a Petition to Establish Parental Relationship with the family court.  This would establish the father and address custody, visitation and support for the child.  You & the dad can also agree on these issues once filed and served. The courts look at what is in the best interest of the child.  It may be a good idea to get legal advice so you understand your rights in your specific situation.