My ex husband did something similar when my son was small, he earned nowhere near what your DH does but did quit his job without telling me (he had been off sick prior to quiting). He also dabbled in share dealing and lost a lot of money and prior to that had racked up some secret credit card debt which affected his credit rating and affected our chances of getting a bigger mortgage.
Luckily although I only worked part time, I did work and I had some equity in the house I already owed so was able to buy bigger in time in just my name.
We separated for a time but did get back together. I wish we hadn't with hindsight.
If your marriage is to survive this, you need to insist on full transparency. He has lied before about your financial situation and will do so again. I am frankly astounded that in your financial situation regarless of how much he earns you decided to send you kid to private school! You cannot afford this. You need to move them asap. A lot of parents who do pay for private education don't do it during the early years, they look at doing it later at say age 9. If you do this now, you will save a small fortune and if your circumstances improve you can save to help pay the fees when they are older - obviously later on you will have 2 sets of fees to pay.
You also need to be involved in budgeting. Presumably some of this falls to you anyway being the SAHM but what is he spending that could be cut back? Can you reduce the car payments. He hasn't proven himself to be good with money so you need to really insist on transparency and sit down together and look at you incomings and outgoings? Presumably he will have to work a notice period so might get another job during that time, even if it pays less (my ex decided to go to uni instead and has never financially supported DS even though it took me a good few years to finally get rid of him).
If you get access to your finances, post on the money board for help going through them and making savings. Also Money Saving Expert has loads of useful advice.
Whatever happens with your marriage, start working on these things now as if you do split and especially if he has no (or lower) income, your lifestyle is going to have to change massively.
Have you never worked? I will just add that I don't think you can fully appreciate how much headspace a highly paid job can take up and how much stress it can cause if you haven't done it and even then, your experience could be different to his. He may just be at the end of his rope. I didn't mind that my ex husband had to give up his job, it was him not looking for another, burying his head in the sand re finances and expecting me to sort it and just generally being financially irresponsible that I found so hard. By the time we separated, I had a full time, decently paid job so DS and I have been just fine.
Good luck to you OP.