K.P.
It doesn't really sound to me like you've got a marriage problem, but a life problem. *Anyone* going through what you've described would have problems, and marriage would not make it worse. But marriage can make it better, because you can have both of you working on the same problem. Rather than viewing marriage as your problem, look at what are your real problems; then get your mate on board with solving the problems, rather than just fighting about issues. Your financial difficulties and his lack of sleep are causing stress and strain on your marriage. Start focusing on *those* problems and then the stress and strain will lessen.
Most likely your husband feels like you aren't supportive enough of him, or don't appreciate him enough. Even if you do support him and try your best to show him he's appreciated. There's a website called "What Women Never Hear" (http://wwnh.wordpress.com) that I would strongly recommend you read, which deals a lot with male-female issues like this. Written from an older man's perspective from what he knows of men and how they think, etc., he gives a lot of good advice on how women can improve their marriages (or make good marriages to begin with). Another book would be "For Better or For Best", (which is the companion book to "If Only He Knew", which was written for men), that likewise helps women better communicate with their husbands, to reach them on their level. Because men and women think differently and communicate differently.
As for the finances -- go to http://www.daveramsey.com for some budgeting tips and sheets and such(he's also on the radio, which can be streamed on your computer from 2-5 p.m. Eastern). You've got to know where your money is coming from and where it is going to, so you can see where you can cut corners and trim costs. And get books on frugality, like the indispensable "Tightwad Gazette" (check for it in your library, thrift store, or used book store before purchasing it on line; then get a used copy, if you can't find it locally), which will reset your brain into thinking frugally (like our grandparents who lived through the Great Depression), and give you tons of tips on how to actually trim nickels and dollars from your budget. It doesn't sound like much, but every little bit adds up.
Is there any way you can get a friend or family member to watch the kids one or two days a week, so he can get extra sleep? Also, pay attention to diet -- make sure your family is all eating enough nutritious food, because if you eat junk, you'll feel like junk. My husband also needs a lot of sleep, but we've recently started "The Blood Type Diet" (http://www.dadamo.com) and that has increased his energy levels and reduced his need for sleep.
Perhaps your husband needs to put school plans on hold for the moment -- less money going out, more time for him; perhaps he could then pick up another part-time job, which would bring in more money; even if he did nothing but practice frugality (shop the sales at grocery stores, cook from scratch instead of buying convenience food in boxes or from fast-food restaurants, etc.), watch the kids, and sleep, that would likely be an improvement over your current lives.