I think you need to adjust your expecations of your parents. The child is yours, your family is living in their home. I don't know what else you can reasonably ask of them. It would be great if they helped, but it's a bonus, not a given. So drop that point.
As far as your husband is concerned, you have to talk to him about it. Earth to brandiriley!!! Seriously, you have to communicate your expectations of him as a spouse and a father. If he's not cutting it, you have to let him know.
Sit down and talk with him about what you need from him. When you're gone and the baby is crying, tell him "try to do X to get her to calm down" When the laundry needs to get done say "Hey - can you throw a load on?" Dirty dishes are piling up in the sink, say "Do me a solid and load the dishwasher." When you need to take a nap, tell him "I'm taking a nap, can you feed her and keep her occupied for an hour?"
Some people will just DO, some people need to be told/asked. Half the time my husband takes the bull by the horns and just does whatever needs to be done. But the other half the time I just ask. Ask and you shall recieve. (I hope anyway... fingers crossed your guy isn't a total slouch!).