But it's not a pitfall of blended families is it? It's a pitfall of redundancy.
If OPs husband and his ex wife were still together and he lost his job - they'd have to tighten their belts until he found new work.
That might mean claiming benefits, relying on her income, taking loans etc. It might mean giving up luxuries, or cancelling some of the kids' extra curriculars or something else.
It would be shit, but it is shit when someone is made redundant. It's rubbish and stressful and scary and there's less money.
It might be temporary, while a new job is found, or semipermanent because a new job pays less, or totally permanent because no one ever gives him a job again. Who knows. It depends on industry, and age, and why, etc. But it's crap and it means tightening belts.
This situation is NO different. The fact he's no longer with his ex changes nothing. He's lost his job, so money is tighter until he finds a new one. As (co) parents they have to cut back.
His new partner is nothing to do with this, and of course she shouldn't pay maintenance. Husband and ex have the same options as before in terms of tightening belts etc. But new partner's income is completely irrelevant.
She might CHOOSE to help, that's a nice thing to do, but not necessary and depends on a whole host of things. She's no more beholden to than other people vaguely related to the children e.g. aunts and uncles (and no one expects them to step up).
The only thing current partner should be aware of and prepared to help with is the husband taking on more childcare while he is out of work. That is his responsibility.