OK, here's a message to my husband - read all of this thread. See what you think.
And that's not to say I think my husband is a walking disaster who is going to inadvertently destroy this family with his lack of consideration - far from it. I'm very lucky with my husband. But he does sound like he has a few of the problems you describe, Emily.
My husband isn't formally diagnosed either, but we're thinking Asperger's. difficult child 1 can't mentally multi-task (although he's getting better at it) so he's learned to carry notepaper and pen to write things down. husband has been doing this for years.
Similarities - husband & difficult child 1 both stress out when not coping. Too much happening all at once is a HUGE stressor. Too much noise, too much light, too much crowd, too much to think about... too many instructions all at once. husband, being older and more experienced, knows to back off and try to consolidate. difficult child 1 is still learning this.
Basically, I have a husband who (unlike yours, by the sound of it) DOES have some inhibitory circuits working in the background. Foreground, probably. While difficult child 1 is much more of an impulse buyer, husband is not as a rule. He copes by being meticulously organised on paper and having (tucked in his long-term memory) a clear picture of our financial situation and a pattern of annual expenditure. He backs every expense up on paper, checks every credit statement and every bank statement. It's something I think he learned to do from his father, who I suspect had similar problems. Doing things this way worked better and so it became the coping strategy. He uses his mobile phone as a personal organiser - as a result he had a record of a doctor's appointment we both had this morning. My own back-up system (which normally works well) had broken down. But it's a habit he actively worked to get himself into, years ago.
With me and husband, we work as a team. The things I'm good at, I do. The things he's good at, he does. And I watch him like a hawk for signs of overload and try to help him plan so we can keep his stress reduced. It doesn't always work. And I know he watches me, too, for signs that I'm overdoing it (even though I think I'm perfectly capable of watching both of us).
Like our kids, when husband is unwell his coping skills go out the window. So we have to accept that on physically bad days, he's not going to be able to manage as well in other ways. I guess that's similar for a lot of us, it just seems more obvious with the males in our family. And also easy child 2/difficult child 2. When SHE'S stressed she goes to pieces so fast you get hit by the shrapnel.
How well your husband copes (or doesn't) will depend on his strengths and weaknesses. I'm fairly sure that for difficult child 1, he is going to need some level of support permanently. He knows his limitations and while he tries to extend himself, he relies on us (or his girlfriend) to support him when he needs it. In turn, he tries to support girlfriend when SHE needs it - she gets emotionally stressed and he works to support her emotionally and in practical ways when she needs it. By watching her, he is learning more empathy and understanding of human behaviour.
With your husband - can he cope with you controlling the money? Would he accept this, if he's prepared to accept that he has a problem with spending and impulse control? Because if so, you may be able to take over this area and rely on him in other ways. Because there are some things we can never change about each other, and the effort of trying is not only frustrating, it's futile. If you bend with the wind and allow yourself to be blown a little way, you can usually do better by changing direction and build some strength in other ways.
I have to help husband in a lot of ways; he helps me in a lot of others. We have to be able to coordinate and mesh together so that together we can make things work. I don't push him to do things that are too difficult for him and I have to vary what I'm asking him to do, according to my own judgement at the time of what he can cope with. It's much the same with the kids. We talk together, we plan together. If we couldn't do this, things wouldn't work.
And from what I've seen, I think difficult child 1 and girlfriend are setting themselves up to function in the same way.
One thing I will reassure you on - if you can find a way to make this work, and if he really is Aspie (or similar) you will find you have a husband with a much higher level of loyalty for you than most. There are benefits. There are areas where I can rely on husband 100%, which is more than can be said for so many other people. He has an incredibly keen sense of justice, honesty and loyalty. He's never had any formal diagnosis or therapy for any AS condition, but he's learned from seeing what works for the kids and is trying to adapt where he can. Not easy for him.
I hope you can make this work. But if you can't, at least you now have a better idea of the sort of problems you're trying to cope with. And if he can't cope with financial responsibility and you can - you should be able to make this work, if he is prepared to accept that you're going to be able to manage it better. If he can put his male ego aside on this one and not feel it's all a personal insult, then there's hope for you all. And many other families do things this way, for a whole range of reasons.
You do what works. That's basically it.
Good luck.