hmm... this thread got me thinking...
I'm one of those household with separate accts and I'm a SAH(almost)M right now. We are able to do so because we sat down and figure out our finances in the beginning. We agree to separate the bills a certain way. For example:
Me - vacations, medicals, extra savings, food & fun
DH - The rest of household expenses plus investments
We both have allowances, because if not how would we know we're making the budget. I'm a little bit jealous of all of you SAHM who can spend anything they want from their joint acct

However, this way of living is working well for us and it curbs our shopping impulses to know that we have to save save save in order to get what we really want.
All the $ coming in is accounted for, which means that we have very little surprises... (I like it that way). Last year when we received a bonus, it was a nice little addition to our savings acct.
And like most of PPs said, any big spending (above $100) for household stuff needs to be agreed on by both and figured out where the $ comes from. Maybe one day we'll be well to do enough to be not as nitpicky about our finances...

But now we are expecting our first child and we would prefer to continue staying out of debt (except for mortgage and his car) for the rest of our lives. Even if it requires a bit more $ monitoring...
To the OP:
My suggestion is write down ALL your finances and future possible spending as far out as you can (maybe until the end of the year). See where you might be lacking and then find time to discuss it with your DH.
I know you said he's stressed but it would be better to discuss it now BEFORE you ran out of $ then later. Then figure out a plan together. Maybe he then will see that you do need the babysitting income and be open to that. Or maybe he'll come up with another suggestions, like redoing both your budget and figuring out where the $ should come from without you having to work immediately.
I think (especially for men), it is better to see numbers than hearing "honey, I think we're running out of $..." speech. If he sees the numbers on paper, it will give a higher sense of urgency than just saying "I'm worried...". YKWIM?
Good luck on your decisions.
ps: I don't think there's a right or wrong way to do household finances (separate vs. joint) as long as you are both happy, transparent AND no getting in debt....