Hi OP
I was in exactly the same relationship until about 2 months ago. We'd been together 7 years, and we only saw each other at weekends. He would say often and loudly to anyone who would listen that we had the perfect relationship - no arguing over who puts the bins out, just the fun stuff. He was open and honest that he liked it that way.
I was the one being dishonest really because I'd smile and agree, but really I wanted the same as you - a normal relationship. Someone to share everything with.
He was always willing to do the holidays, and always willing to see me at weekends, but he is a single dad and works full time, and he liked to keep his life partitioned and me at arm's length.
I let it drag on for at least 2 years longer than I should have, because on paper he was the perfect guy - we have lots in common, and when we are together we have a good time. He always batted away any attempt at a meaningful conversation about where we were going though, and I didn't want to be the nagging girlfriend asking him when things would change.
It sounds like you've got a similar man on your hands. You could describe him as selfish, because he wants the relationship to suit him, but no more selfish than you wanting the relationship you want. It doesn't sound like he's being dishonest, he just likes what he's got. You need to decide whether it's what you want.
In the end I decided it wasn't what I wanted, and I have felt like a weight has been lifted off my shoulders since I ended it. I think it was the guilt of knowing I needed to end it, and hadn't had the guts for a really long time.
It's actually a lot less lonely being single than being in such a mismatched relationship.
Good luck