Hi S.,
Before we had our baby, I knew my husband was going to an awesome father - he loves kids and is great with other people's kids. So you can imagine our surprise when we came home with our crying lump of baby only to realize he didn't have ANY patience for the baby. I mean NONE! He was just as surprised as me! It took him many many months to learn how to bond with and interact with our daughter. There was even a period of time when she would cry whenever he came near her. It was rough going for all of us; I was the primary caregiver and doer of all tasks domestic, while he got to go about normal life as if nothing had changed. When she got to an age where her personality really started to come out (around 5-6 months), my husband started taking on more caregiver tasks more readily. Now my daughter is 13 months old, and has been a "daddy's girl" since about 8 months! Their faces light up when the other enters the room...she runs to him when he comes home from work...he wakes up early so he can spend extra time with her. It took a long time for them to warm up to each other, but now, they are inseparable. My advice (and I learned the hard way, because I am a control freak) is to let him figure things out for himself...don't micromanage how he does things with your daughter - it will make him not want to do anything. Their bond will come with time.
As far as the division of labor goes, I think it is only fair, if both parents work outside of the home, that both parents equally divide tasks at home. You're all working to run a household and family - you can't be expected to do more just because you're the mom! I think that as the baby gets older, and gets on a schedule that is more in line with your family (3 meals a day, regular bedtime, etc...) it becomes easier to parse out tasks and form routines. Now that we have dinner together as a family, we have a whole routine that starts when my husband gets home from work all the way up to when the baby goes to bed. It's nice because I don't feel like I am doing all the work, and while we're taking care of the baby together, we're all bonding and having nice family time. I hope that you and your husband find your stride!