C.O.
ETA: sorry you knew about his kids before you married him, right? Not an excuse. You are supposed to be PARTNERS. You can't ask him to be responsible for money if you are not willing to share the responsibility. That means joint account. If you want - his, mine, ours - so be it. but it's a PARTNERSHIP!!
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We did everything on my husband's income. So I don't know what it's like to split the bills.
When my husband was unemployed - we worked a TIGHT budget and did it together.
Sounds like you and your husband have to have a sit down to discuss finances and expectations. There is NO reason whatsoever that a grown man can't be held accountable and responsible for the FAMILY budget.
If his work is inconsistent - then you need to learn how to budget on your income alone.
Make out a budget on your income alone. See what you can and cannot afford. Go over it TOGETHER. No if ands or buts about it. TOGETHER.
If it means that you need to take credit cards, debit cards and such away. And use cash envelopes - so be it. But you need to get in control of your finances instead of them controlling you. Go to the library and borrow books by Dave Ramsey or Suze Orman and read them TOGETHER.
Money is the biggest issue in marriages. Don't make it one in yours.
Since he is amenable to an allowance. Get him on one. And make him account for his spending. Receipts to account for the money so that you know he's not borrowing money from his mom.
Make sure he's on the same page to keep the family afloat!!
good luck!