So many great women/moms on this site!! They have given you lots of advice and I am going to add a little more to it.
I want to say first that I don't think it is ever really an even balance. I feel that moms do most of what needs to be done. I have 5 sisters and a mom who agree with that. But that doesn't have to be all bad. You just have to put it into perspective and not try to do it all in one day or do it perfectly. Let me add here that I am a SAHM, homeschooler with 3 kids (9, 7 and 20 months). The age gap in kids is due to my husband's 15 month deployment to Iraq. I understand feeling overwhelmed and I still get panic attacks just out of the blue ever since the deployment.
I know my husband will never understand what I do in a day and I will never understand what he went through in Iraq or what he does during the day. I don't care really because his work will never compare to raising and educating children. But as long as we are a family and love each other and support each other, the rest doesn't matter. I have felt like I wanted to leave my husband but it was my mom who said, "Ask yourself, will you really be better off without him. AND will your children really be happy without him?" It sort of put things into perspective.
Living with someone is hard. Think about living with your parents, siblings, roommates. There is always something annoying about others. You have to work at it everyday. It is a full time job. Just remind yourself that you may have somethings about you that your husband overlooks. I am sure that he doesn't notice if things are perfect around the house as much as you do which is probably why he doesn't think to ask if you need help.
Hate is a strong word to use (maybe postpartum depression makes people feel that way)but it does feel like it. It is more like you just need a break. Right now I get to go to the grocery store by myself. It may be for 2 hours but it is my time. Gas is so expensive and we live in a rural area so I don't get to just go shopping for clothes but getting the groceries is some time for me. I crank up the songs I don't like my kids to hear:)and I take my time.
I have been married for ten years and I remind my husband that our sons and daughter will look to us as examples for their own spouses. What do we want them to see in us? I want our 2 boys, especially, to understand how hard a mom has to work. We do a few things that really help us. First, we are affectionate with them and each other a lot. Second, we always go to church together as a family, no excuses (unless someone is sick). Third, after dinner, everyone helps in some small way so that we can sit together a little while before bedtime. Even my husband vacuums, or picks up the plates, or feeds the pets. Anything. I explained to him that his job ends when he comes home. My job is 24 hours a day. If he doesn't want to listen to me "nag" (his word) than he needs to help me shave off at least an hour or two. It isn't perfect but it isn't boring either!!
It won't fix itself overnight but hang in there. Ask any single mom what they go through. Try to hang on to what attracted you to him in the first place. The sex part will come and go in any relationship. There has to be more to your marriage - it will come back. Someone mentioned the pill giving them trouble. It does change your hormone balance so don't think it isn't possible.
Good luck and God bless (sorry this is so long)
Z.