I live with my parents, and my boyfriend moved in April 2016. We have a baby but we never married. Am I able to file as Head of Household? He's claiming our baby as a dependent, am I eligible for child tax credit?
When you check the links that AndreaC1 provided, you'll see that one of the requirements for "Head of Household" is that you paid more than half the cost to run your home.
Also, please be aware that when parents live together only one parent may claim the child for all tax benefits. The parents cannot choose to split these benefits.