I found the whole birth experience very surreal and my baby needed to spend his first night in intensive care so he was whisked away from me so quickly (and my husband went with him initially)...So in some ways the experience was more real for my husband than for me.
We also found that we argued a lot more than usual - about routines for the new bub - controlled crying and the like. The downside of a hands on Dad!!
SB2
I think this brings out a good point of what type of birth and labor experience you have. My husband did a lot from day one because I had some bad health problems because of the birth. It's also his nature to be a helper-type--he enjoys doing--helping people out. Also, I had some really severe post-partum depression for at least 3-4 months. So, my husband, with the help of his parents, often became the full-time parent. I would say that it took much longer for me to strongly bond with my son than it took for my husband. And I was even breastfeeding. Breastfeeding in itself is not always the ticket to a strong bonding experience between mother and child, actually.
As far as fighting goes--we fight much less now, after my son was born. My son required (and requires) so much time and energy that we don't really have time to squabble like we used to--we'd rather just solve stuff quickly. It also helped that we were really in agreement about parenting styles overall and discipline. The only big difference is that my husband is a bit as my mom would say "OCD" when it comes to certain things and insists on doing things like bundling my son up like a blizzard is going on as soon as it gets a bit cooler in temperature. But, we actually don't fight about that stuff. Somehow, having a baby brought chaos to our house in a way but at the same time brought some more tranquility to our relationship.