I'd say your family height is more indicative of your children's height than your height. However, don't forget, your wife has quite a bit of influence, too. If you want tall children, choose a tall wife.
My husband is 5'7". He was not sick as a child, as far as I know. His father was 5'8", and his grandfather was 6'1".
Our two sons are 6'1" and 6'2".