Skeptical of husband handling household?

I work full-time 12 hr shifts 3 days a week. My husband has been laid off for 2 years. He has gotten much better recently in our 11 year marriage. We have 3 children, 16, 10, & 8. During our first 8 years of marriage my husband didn't mop at all. The house cleaning was left to me and the kids while my husband pursued many business ventures/career changes. When he was working I would come home from working night shift in the morning there would be dirty pampers, dinner dishes on the table, etc. When I would complain he would help clean up but it was not consistant; without my complaining or getting mad he would not clean. Now I frequently help kids with homework when I get off work, we share the household responsibilities 50/50. On my days off ( 4 days a week) I still cook dinner/breakfast/lunch while working full-time and I am currently taking classes. I have conveyed this to my husband and even told him that I am so stressed out I have started to notice that I am getting sick ( colds/flu) more frequently. My children are all very active in year round sports. He seems to think that our oldest 16 should cook dinner and clean the entire house & often complains I'm not teaching her how to "maintain a house" ( cook, clean, etc.) We have chore list for each child, but they don't follow the list unless you check up on them each day; which he rarely does and I do sometimes after work. I really think that since he is at home, he should do these things since our kids practice until 8pm on most weekdays and are gone every other weekend with their sports activities. I would love to further my career. I have always put off going back to school to let my husband pursue his dreams, but now it is my turn. I have an opportunity to go back to school for about 3 years and triple my income. The problem is I cannot work at all while I'm in school and I would be away from home about 60 hrs a week not including time needed to study. This would mean my husband would have to work full-time and provide the primary care for our kids/home. I have conveyed my interest to my husband to go back to school and he is very vocally supportive. However, I am still doing majority of the work with the house/kids and he is not even employed. I worry that if I get started in school, he will not be able to handle the house and kids. Schooling is very expensive and once I start I would have incurred loans/debts so I must finish. I worry that no one will be there to help study spelling words, or help with science projects, or cook nutritious meals for the family. He assures me he can handle it but how can I believe it if he can't even handle all of the household and he is at home 100% of the time. I have talked to him till I'm blue in the face but he assures me he can do it. I am very skeptical. What can I do?

Updates
Let me be more specific. I am truly not a neat freak. I do not expect the house to be emaculate. On a scale of 1-10 (10 being very clean) my house is probably a 4. I would like the house to at least be maintained at a 7. I realize with 3 kids and a dog the house will get dirty but I think a consistent collective effort should be made to keep it clean. When I say clean I mean basic sanitary issues such as no food on the floor, the bathroom should not smell like urine, the house should not smell like old garbage (because no one takes the trash out), and clothes should not fester for more than a week in the laundry room without being washed. I would like kids homework/ projects to be complete and chores to be started. Mind you my kids are old enough to do all of this they just need reminding on a daily basis. As for school I am in the medical field in which I work 12 hrs 7am to 7pm most of the time without lunch/breaks constantly on my feet. The program to which I hope to attend requires school ing 3 years. During the first year the program requires only full time class attendance so I can work for the first year. The second and third year the anticipated class hrs are about 60 hrs per week not including the 1-2- days I would be oncall ( be in the hospital 24hr- yes sleep there) very much like a doctors residency program. During the 2nd and 3rd years of school students must obtain consent to work ( must be in good academic standings). School is year round with 1 week off in the summer and 1 week off in the winter. The sacrifice is tremendous but this is something I have dreamed of doing since my early college days. I put my aspirations on hold for my kids and for my husband to pursue his dreams. I really want this and no I can tolerate a dirty house but helping the kids study, unfinish homework/projects I would feel very guilty.