I am so sorry you are in this situation. He's betrayed your trust with this financial abuse.
You are in debt if you still owe money on a kitchen, Argos card and a sofa or have a car payment - even if at 0%. These are expenses that you didn't have money to pay for when you bought the item, and do not have the money to pay off today.
Lots of good advice above. If you are staying in your marriage, he needs to go to marriage counselling with you, have open book accounts and letters re anything financial including pensions, to add your name to the rates and any other communications that affect you. He also needs to explain his financial support for his parents so you can make a plan for that, repaying the rates debt, pensions and household management (including emergency funds) you are both agreed on.
I would credit check yourselves - him and you, just to rule out credit cards you don't know about. People who are bad with credit are profitable, so him having a card doesn't mean anything about his credit status. Check the house is in joint names and that there are no charges on it (security for debts that must be paid first if the house is sold). You also need wills and your name on any death in service benefits and pensions he may have - so you are sure what happens if he dies. If you are staying, you need a plan about pension provision - as you'll be looking after his financial needs when he stops work. Financial management and planning must involve both of you.
I've learnt a lot from using YNAB. It's a budgeting/money management app that has helped me realise how much we need to have, not just for maintenance of our house, car etc but also replacement of white goods, tech and our car and if our income stops. I've found debt reduction style youtube videos useful. I don't agree with Dave Ramsay's religious views and that marriages must have fully joint finance - but there's lots of useful process to learn from his channel, not just about digging oneself out of debt, but also target savings for replacements, Christmas, and pleasure (holidays, adult and children's hobbies and activities and doing up the house or having a new sofa etc), pension provision, living expenses if one or both partners lose their job or can no longer work. This will enable you to understand what will keep the kids' home safe - even if for a while the extras for the kids and meals out are stopped or reduced for a season. It's their security and your sanity that matters most.
You sound like an amazing mum, and have great skills to get you and the children through the next bit. I hope you have friends and family who can support you when you know whether he will work with you, and as you develop your plan to manage. Good luck with managing this and your job.