You've already gotten some great advice and wisdom from experienced moms! I'll add a few suggestions that I've found can help.
Sittercity.com first of all. When you're feeling better, check it out, interview a couple of girls in your area, have them meet you and the kids and now you have a few sitters when you're in a pinch. Try them out while you're home a few times. Call you neighbors and ask for their sitter's numbers. But, you have to have emergency backups for yourself.
This is true for your husband as well. He has to have an emergency backup for himself at work. Maybe you can bring it up to him this way - I have to have a backup for myself, so I'm going to find a few sitters that I can call on. Likewise, you have to find a backup for yourself for family emergencies.
Let your hubby know how much the sitter is going to cost so that he has something concrete to weigh it with next time :). Money talks with men. They worry about providing. They really worry about providing. And, it looks like he is probably paying child support for his 4 other children as well. That's a lot of responsibility.
Finally, find other things he can do on his schedule that will help you. Ask him to go to the store on his way home so that you are equipped for the next few days (frozen dinners, soup, juice, milk, fruit, etc). Ask him to pick up a couple of movies from Blockbuster so if you're not feeling well, you can let the kids watch them. He probably doesn't have to leave right away in the morning, so ask him to get the 6 year old off to school and take care the 2 year old so you can sleep in...etc.
I really hope you're feeling better soon!!