I agree with getting him to research the details in full. Say you will only consider it when you know the full picture in terms of actual costs, logistics and what his package will cover in full.
This includes exactly what healthcare costs will be including the existing conditions and dentistry, also schooling fees, transport there and shipping of any belongings, accommodation, transport when you're there, any storage, letting out the house if applicable, living costs, visas, your rights to work (importantly). If you can work then ask him to find out local job prospects for you- who the major employers are in your field.
Tell him you're not ruling it out but don't want to discuss it again until he can produce this information in full and it is feasible, not just 'oh well it must be ok or they wouldn't be offering that' as though some employers are not shit. All this information will take a fair bit of research, probably calls to the embassy, schools and insurers etc but if he is serious then he needs to do that and prove that this is something that will benefit/ work for the whole family, not just an escape route for him.
He sounds depressed and looking for an out and has latched onto this as the answer. Your objections will just come across as obstructive but if he does all this research to brief you himself and realises it's not doable then it isn't on you. Could be that it is doable, or that he wants a stint overseas and it is possible with another employer who pay better. If so, I would keep an open mind (depending on your rights), but he has to put the legwork in, not you. He can't just expect you to sacrifice your career.
Also yes to reading up about the Hague convention and travelling with children if your relationship breaks down as he sounds quite unstable at the minute in himself. I don't know the details but you should.
I would also not rule out letting him go alone if he is that desperate, as long as he pays his share to the household and kids here as well.as covering his own healthcare so you're not stuck with any huge bills. If you let him know that's an option then, again, you're not being obstructive but it's all incumbent on him. I wouldn't be too surprised if he is actually relying on you preventing this happening and it's out of his control if that makes sense then he doesn't have the responsibility of making changes.