I'm sorry to hear that... It is a struggle I go through as well at times. If we didn't have 3 more kids I may not even be with him.
Thank you for clarifying your situation. I hate it when my girlfriends pull the momma card out only when it comes to correcting bad behavior in their kids. And I have more than a few that are happy to have their boyfriends give their kids everything under the sun but then tell him to back off when their kid does something bad.
Your situation is different because he does nothing else to help you out or be a part of your family. In my case I have had to weigh the pros and cons. He does love our kids and does provide food and shelter, etc. He just doesn't get involved with much of anything else in our lives. In fact I have to ask him to discipline the kids at times because he tunes everything out now.
But I feel that if your boyfriend does nothing and he isn't a very good boyfriend anyway, boot him. Replace him with someone (like a college kid) that needs temporary housing and can help out and pay some of the bills.