T.H.
First I have to say to AC...wow, you must be married to a saint! I love my husband and we have a great relationship, but what you're describing could be my life!!! This is more the norm than not, I promise you that.
Not sure how old the baby is but the first 3-6 months of the baby life is a killer. You are both sleep deprived and that will make you crazy...literally. You have short tempers and you're still emotional, something that he may try hard to understand, but honestly, never will. Women think about things SO much differently than men and although I find myself thinking some of the very things you're describing, I try and remember that men are seriously clueless about these things...and I guess what I really mean is that the things that are important to us are not important to them.
Just like Denise said, as hard as it is (because I know you're thinking how can he NOT know the dishes need to put away and how can he NOT see the pile of clothes he just stepped over, etc.) you have to ask him in a nice, calm, normal voice to do the things that you want for him to do. Tell him what will help you and what stressed you out. He doesn't know, even though you think he should.
I'm sure that you had some of these issues (like trying to hold any sort of conversation while the TV is on) before kids, but kids adds new stressors and new things on the to-do list, so it's different.
You are not alone, but you do need to talk to him. Don't expect huge changes and do expect to have this conversation with him at least 3 more times before the year is up, but talk to him. Tell him what you want and need.
Also, get out of the house! Try to go on dates or if the baby is too young to leave with a family member or sitter then at least try and plan some at home things like movies or ordering in or game night. When my hubby and I are feeling disconnected we open a bottle of wine, get some cheese and play a mean and ruthless game of Scrabble! it's so silly but it's fun!
Let me just say again, that as obvious as things seem to you, they are just as unobvious to him. Talk to him and it will get better!