Why should your partner not cover the cost of things?
If it's in the short term? Say 8/9 months, you can either save up the maternity allowance to plug your savings hole, or just use it as income for the baby.
He's equally a part of creating the baby, so has he been equally saving? Putting money aside each month to cover the cost of time off?
Plus, presumably if you were working you would need childcare, and you will be saving a fortune on fees for childcare by being on maternity leave so you can just redirect that money into bills.
I do understand some people dislike the sentiment of partners paying for everything, or feel it should be equal or split in some way based on income, but given all you will be doing for baby I don't think it's unreasonable for greater financial contribution from your partner.
In my house my partner covered all bills, and then I used maternity allowance to pay for baby classes, lunches out, new baby bits and bobs and monthly food shops. When I'm back at work this will change back to contributing towards bills, based on my income and also how much childcare I do.