My boyfriend does this almost exactly. He does three 12 hour shifts at a hospital (he's not a nurse but does nurse support stuff). He does about 2-3 overnights/month and about 1 weekend/month. So, he's generally home most weekends, and he's not too affected by the overnights since they're not that often.
We don't have children though, so I can't speak on that. He is exhausted after a 12 hour shift though. He has been finding he can't/doesn't want to do much the next day. Or at least will wait until 2-3oclock to do errands, gym, etc. He is on his feet and busy the ENTIRE 12 hour shift though and has one half hour break for lunch. I don't know how he does that. I need to eat every 4 hours at least, or I go nuts.
I don't know, I guess there's pros as cons. Having 4 days off is awesome, but they're not consistent which will I think is a major drawback.