I am a SAHM, we have 3 DC - one primary school age, one preschooler and a baby. DH is generally out of the house by 7:15 and is rarely back before 8 at night, and even then will then often have to work from home (conference calls, emails etc) till 11pm or later.
So with the best will in the world, there isn't an awful lot he can do to help with/take over/provide support with the DC during the week. I pretty much fly solo with all three of them on my own in terms of childcare and running the house from Monday to Friday. Sometimes DH might get home in time to read with the older two, but it's very much a sometimes, not always. He only sees the baby briefly in the mornings during the week, as baby is always in bed by the time DH gets home.
At weekends, though, we split most chores apart from laundry which I manage (he would put a wash on/hang it out/bring it in if asked, but wouldn't do anything unless asked, if that makes sense). I probably do a lot more in terms of keeping the house tidy but that's mainly because tidiness bothers me a lot more than it bothers him! But he'll do the week's shop or put the online order away. He'll do mealtimes and bathtimes and change nappies and read stories and take the DC out to the park. We take it in turns to have lie-ins, if we want them. We try and ensure we both get a bit of time out from time to time. And we've always had a kind of unwritten rule that one of us prepares a meal and the other washes up; during the week, it's generally me cooking and then DH washing up; we reverse roles at the weekend as DH does all our cooking then. And DH has always done his fair share of night wakings, too - not night feeds, because I breastfed, but any other wakings (illness/teething/nightmares or whatever) have been split between us.
OP, I don't think you are being unreasonable in feeling that your DH should help out more, but I do think it depends on the nature of the job that the main breadwinner has. If DH got home at 6 or 7 as a matter of course, I'd definitely be expecting him to muck in and help out! Our issue is that the demands of his job render this pretty much impossible during the week. I can't imagine how different it would be if DH had a job that enabled him to come home in time to help on a regular basis; I have friends who say things like 'I find it really hard because DH is never in till 6pm' which has me completely
; that's not hard, it would be like a flipping holiday
. I am resigned to always managing the midweek bath and bedtime routine on my own. But that's just the way it is for us; life is full-on and we both work hard but it always feels like a partnership.