In the parent case he's talking about 'academic' families, instead of biological families (academic meaning that the 'parent' is the academic advisor of the 'child'). Of course, having several members of the same family all receive Nobel prizes is quite exceptional (and I believe unique to the Curie family).
I really like the German word for PhD advisor, Doktorvater (http://de.wikipedia.org/wiki/Doktorvater), which reflects this "family" aspect so well. I wonder if other languages have similar nice terms for this concept. BTW, Wikipedia says Doktormutter is also sometimes used.
Sorry, didn't know about that. And yes, the Currie family is exceptional but according the the Wikipedia link there are several husband/wife or father/son combos that received the same prize.