I'm a faculty member in a very demanding PhD program where we only rarely have students who already have kids. I worry about those students, and I recognize that I couldn't have thrived in my own doctoral program if I'd had kids then. The first semester, in particular, is brutal for everyone. The reading load is just SO heavy and the type of reading is so unfamiliar. (I'm also a bit concerned that your spouse is already feeling overwhelmed, and we haven't even gotten to the real crunch at the end of the semester.)
So, from my perspective, you're in a situation where everyone is right to be overwhelmed. Here are just a few tips:
(1) Streamline your parenting--meaning, take all the shortcuts you said you'd never take (frozen vegetables rather than fresh, missing a few soccer games, skipping back to school night, whatever).
(2) Encourage your husband to "work smarter not harder." I work on this with my grad students a lot. Some concrete tips: devote a set number of hours to reading for a given class, and whatever doesn't get read in that amount of time doesn't get read. (I find that it usually all gets read if there's a clear boundary!) Do his most taxing intellectual work (reading/writing, usually) at his best times of the day, and save the mindless stuff (grading, sorting citations, entering data, whatever) for the less productive times of the day. Figure out which are the tasks that expand to fill the time available--for new TAs, that tends to be course/lesson planning and grading--and set clear boundaries on how much time to devote to those tasks.
(3) Know that this is just a season. The first semester is universally the hardest. Assuming your spouse is on an assistantship, he's having to adjust to the demands of coursework AND research or teaching. Those are just really big transitions. The remainder of coursework should even out a bit (and then there may be another intense period if he has to take comprehensive exams).
I've been assuming here that he's in a PhD program, but I suspect there are some commonalities with law school, med school, and other professional degrees as well.