92AP has pretty much put it perfectly.
The is no such thing as a 'normal' relationship, it's what works for you.
Communication is key, even when you're unhappy TALK, even if it means making a cup of tea and sitting in another room for 10 minutes to chill first.
Sharing chores, sometimes I do more than him, sometimes he does more than me (except cooking, he has almost burnt the house down one to many times)
If you live together, shared finances help (doesn't work for everyone, but it does for us, it didn't with my ex) we have joint accounts we put equal money in to one for all of the bills, Inc food shop and fuel, the other savings. But we also have separate accounts for our disposal incomes, mainly because I'm big on where spending is going and if I could see where he was spending money, I'd know what I'm getting for my birthday and Christmas 😂
On the child care side, I'm yet to experience as our first is due in July, I suspect until I go back to work I will be taking responsibility for most of that, and probably do most, if not all of the house work too, but I'll be here to do it while he's at work, so it just makes sense (this could all go wrong because you know, best laid plans etc)
We both work full time Monday to Friday, he goes to the gym every weekday evening, so the weekend is our time. Even then sometimes the most we spend together is when we get up, go to bed and eating lunch and dinner (he's a gamer and I'm a big reader, so we can be in the same room and only conversation is "drink?")
But as above, it's not healthy or normal to feel like you can't talk about things. If you know you can do that, I wouldn't worry too much.