I'm in the opposite situation. We have 3 children and I could see us having one more. Hubby says he's D-O-N-E! So, in my opinion it's up to him to take care of the birth control - whether temporary (condoms) or permanent (vastectomy).
I don't think you should have another child if you don't want one. There are many kinds of birth control out there that are not-hormonal. I've heard the Mirena IUD is a good choice. It lasts 5 years and isn't supposed to affect future fertility.
You need to talk to your doctor about options. Then, talk to your husband. Tell him how overwhelmed you are. How, despite how much you love your children, you feel your family is complete. Not to mention the fact that, by the time you're 50 your youngest should be OUT of the house!