Dad: XNTP (Appa, you actually may be an 'E'...omg)
Me: INFJ - duh
I've thought of this very topic. I'm no expert, but I will say that my dad is highly intuitive. As a funny sidenote, his aura photo and mine were nearly identical, and I've also been told by three psychics (two unsolicited btw) that I'm highly intuitive, and I KNOW I am...I'm starting to own this about myself. I see that intuition in my sister as well; we're both listening to our Nis like a mofo.
My mom and I share that Fe, and we tend to be the softies in the family, but I also see a lot of strength in that because we're able to put aside our pride more easily than the NTs in our humble clan (no offense Dad & sis). Anyway, I believe I was meant to be a part of my family; we all bring something of value and each of us fills a strength where another has a weakness.