Any mothers out there with step children?

I'm getting kind of frustrated with my boyfriend. I need this job I have, and he's been putting all sorts of restrictions on my hours because of him watching the kids. He says it's hard on him because he wakes up at 4am, sometimes 3, then has to watch the kids, which I totally understand so I have does as he's asked. Two of them are mine from my last marriage. But, because he said he can't, physically and mentally, watch the kids right after work, I don't go in until 5 most days, 4 at the earliest. But if I don't get home from work at 8, he gets very upset. I don't understand what the big deal is. On my days off, I'm with the kids almost all day. He'll be at work, then comes home, takes a nap, and practices on his guitar until 6. So I feel like I watch the kids way more, because I only work 2-4 days a week, mostly 5-9.
But, I am the mother to all three kids, so I don't understand the feeling of watching "someone else's kids." While he claims that he sees them as his, I can't believe him if he throws such a fit when I have to go to work. So, I feel if he truly sees them as his, it shouldn't be such a big deal, right? I dunno. I just need a different perspective. My daughter defiantly sees him as her father, since we've been together since she was six months old. My oldest does remember his father, and when he sees pictures or talks to him on the phone (very rarely, like a few times A YEAR) he calls him daddy, but I think he thinks that Grey (my boyfriend's name) is what all dads are called. He was 1 1/2 or 2 when we started dating.

Megan GibbsMountain Home, Idaho
    My husband never has the kids...and they are both ours together. I think it's just different for some guys.
      Comment deleted
      Megan Gibbs
      That makes sense. We've been together for about three years, and it's always been a "I have have to go to the store-fine" sort of thing. But he hates leaving the house more (he's such an introvert lol). Before our baby was born, he made sure to let me know he never wanted children when he was drunk. But now that he has one, because he also said that if he did get a woman pregnant he'd be there, (turns out he's a pretty good dad) he's really stepping up, but still has a problem with the other two.
      About Megan Gibbs
      Current: Mountain Home, Idaho
      Birth: June 13
      On since: Apr 16, 2014
      Finally got a job. Jack in the Box. Not much, but it's something. I'm divorced but in a new, better relationship and he's my new son's father. I'm very happy to have him in my life (my ex is a free loader, currently living out of his car).