G.♣.
Everything you are experiencing is completely normal! You aren't doing anything wrong, and if anyone you know says their baby slept more or slept through the night at that young age, they either don't remember correctly or they were just one of the lucky ones.
We co-slept with our kids. I think they sometimes wake up just because they want to know they aren't all alone. Sometimes one of our kids would wake up and just touch us and go right back to sleep. When my oldest was a baby, I even started nursing him to sleep in our bed for naps. I would just gently roll away when I saw that he was really asleep.
I don't know how i would have survived those first few months if I hadn't co-slept. It really was a lifesaver. I actually got to sleep for a few hours!
Also, Dad needs to let you take a nap once in awhile and sleep in once in awhile. If your daughter will take a bottle, let Dad give her a bottle (breastmilk or formula - whatever). Mom needs to get some sleep once in awhile.