Separated in NC (agreement, not court ordered),different addresses and kids involved. Can we file joint, and my girlfriend file Head of household? (lives with me)

[derkwad]

Background:
Separated Dec, 2015 with separation agreement (NC), lived separate and apart since.
2 kids from marrige.
Filed joint in 2016 for 2015 return.
live with girlfriend at different address march 2015- current
she pays bills, I stay at home dad. 
I have a child with girlfriend Oct 2015.

So we are trying to see what are options are for filing, mainly being trying to receive the earned income credit for all 3 kids.

Question: Can I file Married Joint and be able to claim 2 kids from marrige, and my Girlfriend file Head of Household and receive the earned income credit for new child in 2015?    If not, what is my options? 

[Opus 17 · Accepted solution]

With your legally still married spouse, you can file jointly if you both agree.

Your girlfriend can file and claim your child together (child #3) if you do not claim child #3 on your joint return with your spouse.  Your girlfriend can file as HOH instead of single, as long as she pays more than half the cost of maintaining the home where you live together.  This does not mean she has to earn more money than you, if the money you earn goes toward your first family.  But you will want to be sure that your girlfriend actually does pay more than half the living expenses for your new family, in case you are audited.  Your GF would also qualify for EIC if she did not pay more than half the expenses and filed as single with child #3 as her dependent.  (The only filing status disallowed for EIC is married filing separately.)