This is quite complicated, isn't it? And, although you say his attitude to you is a cause for your depression etc, I wonder whether you've realised there's a lot of chicken and egg to this situation.
To begin with, you need to tackle the immediate situation.
To start with, as PP have said,you need to deal with the issue of the 'household' accounts. You should have enough money to pay for essentials and half of it, at least, should come from him.
As a suggestion, set up a joint account that all these expenses are drawn from, direct debit as much as you can and withdraw X amount of cash a week to cover the rest. Put the cards (both of you!) in a drawer (or a safe!) and don't use them! This is also the account that both of your salaries and any Benefits you receive should be paid into.
Then, sit down with your DH and work out an equitable way to budget the rest of your finances. Set up two more current accounts into which you both get a set amount of apending money each month. This is the only account that you should carry plastic for - ever!
Get rid of the credit cards, right now. Cut them up. All you're doing is creating more debt. Being horribly blunt, you carryng a credit card is the equivalent of an alcoholic carrying a bottle of whiskey in their pocket. Sooner or later, they will drink... and you will overspend.
You should have access to enough money to make reasonable repayments on your debts without being completely broke or struggling to pay the bills if, as a family, you are in a position to do this. Anything else is short-sighted of your DH - there's most likely already a financial link between you and every time your credit rating takes a hit, so does his - and leaving you short will make you dwell on the issue.
Unfortuantely, what you can't expect him to do is repeatedly bail you out. That would be facilitating your addiction on his part and not very fair of you to expect. You must continue treatment and he must see you making an effort to change. You may want to consider counselling for both of you, just to give you both a chance to be blunt about your perspectives on this particularly if, as you say, he has his own background causes for being touchy about money.
Now, here's where it gets chicken-and-egg and here's where I'm likely going to upset you (I'm not trying to!) and get myself ripped to shreds by other posters!
You cannot expect your DH to not be controlling of your finances when you freely admit you can't be trusted with money. He'd be mad not to keep an eye on things.
And, although it's not right that he belittles you, you may have to bite your tongue a little bit and accept that he's lost respect for you because of your behaviour - and that something of that is showing in his attitude.
Every time you get yourself into more debt, you put your whole family's financial security into more jeopardy - including your children's. So far, it doesn't sound like there have been consequences beyond you getting a few warning letters - but will that continue? Sooner or later, a creditor will come banging on the door who won't accept anymore missed payments or what have you and will start threatening legal action. Legal action that can include court orders, bailiff's, and respossessions. You simply cannot expect your husband to be sympathetic about your exposing your children to that risk!
You have a right to expect him to support you whilst you seek treatment, but it sounds as if he has been, to some extent. You say he's paid off debts for you in the past, for one thing, which, again is as it should be, but only if it makes a difference in the long run - which it doesn't seem to have.
You say you shouldn't have to apologise over and over - and you shouldn't, if it's only one incident that your husband won't let go. But if you're repeatedly doign the same thing, then apologising, then tbh, yes you should have to apologise (unless you think it's fair that your DH has to accept your behaviour?) and you should also be willing to realise that your apologies are probably meaningless.
This is why I'm suggesting your both go for counselling. It's no different than any other couple struggling with an addiction in one of them.
I'm sorry for being so harsh... but perhaps go and have a look at all the threads which start 'My DH keeps drinking or whatever...' and see what advice is given to the poster's there. Your husband should support you in treatment and he should be willing to draw a line under the past and move forward without holding it against you whilst you make the effort to seek treatment but it has to be a two way street, I'm afraid, and you need to make some of the effort to earn back the respect you've lost from him.