Fighting in front of kids is bad, it makes them think fighting is the answer to everything. It's what makes kids violent, and in general, harder to deal with, and less likely to listen.
I definitely believe that they can hear you, even when sleeping. I remember, when I was young, I would always wake up when my parents were fighting, and they never yelled at each other. They just had heated discussions, but for some reason, I could feel it and it would wake me up. So, I'd sit up and listen to them argue for a couple hours, and then go back to bed after.