My mom is an ESTJ (who did almost all the parenting single-handedly)
My dad was an IxTJ (perhaps INTJ. he gave financial support, hung out with me on some weekends, and now he's dead)
I'm INFP. Me and my mom are extreme ends of the same pole. I'm not sure if I did inherit her preference for Te-Fi and Ne-Si, but it would be mere conjecture to say so. However, according to a friend of mine, his INFP girlfriend's mom is an ESTJ(the same case with me). So...I'm not really sure where I'm going with this but I feel that there might be some truth about function preferences being inherited and all, at least to some degree.