I'm presumably an INFJ, and my brother is an INTP. So it's the reverse of your example so it doesn't apply so much. But I'll mention my parents anyway. :-)
My mom is definitely an ISTJ, and I was never quite sure about my Dad - I lately have been considering him an IxTJ. However, I just consulted with my brother, and we both agreed he's rather different from Mom in several ways, and after my brother read the INTJ description, he said, 'That's Dad...but I think Dad's just learned not to express his opinions about things.'
Mom has had difficulty in general understanding my brother and I, and is perhaps the most difficult to have positive interactions with - there are just lots of potential areas of misunderstanding. My Dad is more of an interesting case; his father was a hardcore INTJ, and many of his INTJ traits shone through his entire life and he kind of rode his family hard; so my Dad I think has consciously made an effort to not be so much like his father. (no offense to any INTJ's out there, by the way - incidentally, I held great respect for my grandfather as a child, it's just I would not have wanted to be his wife or child. But also, it was a vastly different generation too, so there's that).
So anyway, I'm babbling, but yes -- parents have a profound influence on their children. I don't think I myself was terribly healthy for a while, and had a lot of identity/confidence issues, and still probably do to a certain extent -- just not nearly so much as I used to. My brother was also extremely unhealthy for a period; at age 19, he was actually in a hospital for about 6 weeks because he was suicidal, and was in therapy and on meds for several yrs after that, but appears to be doing MUCH better now. Regarding my brother, who really knows. Was it family dynamics? Was it his own thing? Was it more of a chemical imbalance? It's anyone's guess.