Agree a "rent" amount with him and transfer this to his account on a monthly/weekly basis. You should ensure that you are getting rent relief as you are not getting Mortgage TRS.
He should pay house insurance, house repairs, major fittings (furniture etc)
Set up a joint account to which you both contribute equal amounts. This account should be used for all utility bills, TV license, and your weekly shopping. You'll need to figure how much you'll need to fund the account with to cover everything. Get a laser card on it, so that if you do pay some groceries or the cleaner with cash, you can take the cash from the account.
If the joint account works well, you could attach a deposit account to it and start to save for holidays or maybe even a wedding ;-)
When the baby comes, you need to decide what you'll do with the children's allowance. I would imagine, you should agree to fund and the joint account a bit more and put some of the children's allowance in there and put some away for the child if this is affordable. You'l also need to agree with him that you have to cut the rent transfer as presumably, at some stage your salary will be reduced when you are on maternity leave.
For functions, restaurants, presents & other non routine, I'd let who is most flush at the time pay.