Realistically, how much housework are you talking about here, for a one-bed flat with two adults and a baby? Because I'm a bit lost as to what will be left for him to do half of?
Once you eliminate the daily cooking-washing up-childcare components, what are you left with in a week? A couple of rounds of dusting/hoovering in a couple of rooms? A good bathroom scrub once, same for the kitchen and the loads of laundry - one a day, maybe?
He should be doing half the 'daily' chores at weekend, because you're both in the house, so stuff like cooking, washing up, and any laundry that needs doing at weekends. He should also be doing half the stuff for your DC at weekend, if not slightly more because he's not free to do it during the week, being at his job. You should also leave your big weekly shop until the weekend when he's free to help (or order it online!)
But, you might be being a little unfair expecting him to help with more housework at weekends. Is he literally going out to work, coming home and doing absolutely nothing at all during the week, including never changing a nappy? Because only then would you be fair to ask him to do half the 'big' housework as well.
If you're really struggling that much, perhaps you need to sit down and look at what actually needs to get done/when and how you're doing it etc as a family. You may find that the issue is one of planning and routine rather than a genuine need.
Also, start giving some thought as to what will happen if/when you go back to work full time.