Is your partner's income spoken for each month? I only ask because you say that you each pay half the rent and I'm wondering whether he could pay the full rent.
I realise that some couples prefer to keep completely seperate finances and contribute equally to the household bills. However, if one person's income is more than the other, particuarly in a situation where one parent is looking after children, it might make more sense to change how you calculate how much each person should contribute financially (i.e. not 50:50).
You are a family unit with a newborn on the way, not two students sharing a flat. Its perfectly fine for your partner to pay 75-100% of the rent at a time where your income is reduced, your contribution to the household will be in caring for your newborn.
I realise that its difficult to manage on a low income, let alone smp. However, will you really be any better off if you are back at work and paying out large sums for childcare? Or do you have family who will provide childcare?
If DP's hours/income mean that you cannot get benefits/tax credits then it suggests that they ought to be contributing more to the joint finances.
Apologies if your partner's income is already swallowed up by joint bills but there are women in situations where they are at a financial disadvantage to their partner either through pride (which is misplaced if she is contributing more to childcare or other aspects of the relationship) or through their partner being controlling.
Do get advice about working tax credits and child tax credits, as the number of children you have will affect what you are entitled to - so the new baby will change the limit to what you can earn. e.g. my DH and I aren't eligible for working tax credits (just), but we are eligible for quite a bit of child tax credits once our baby is born.