Was St. Joseph free from original sin? Yes, I do believe he was. This is only logical. Since Mary was immaculate at her birth, and Jesus was of course free from all sin as He was God, why would God put in place a husband, stepfather, and protector of the Virgin Mary and Jesus that carried original sin? This doesn't make sense. That which stained by sin does not oversee and protect the pure, therefore at some point Joseph must have been immaculate also. St. Joseph was not just the member of the Holy family, but he led the holy family, and what we forget is that while Joseph lived, Mary and her son Jesus were obedient to him. As God is never subject to sin, then logically St. Joseph was immaculate also.
The only question is when? When did God make Joseph immaculate. I don't think at birth, because I feel strongly that he had a family and was a widower when he was chosen to be with Mary. So not at birth, but later...but when? Perhaps, as God is very efficient, and usually when God moves, it is for more than one purpose, I wonder if when the lily grew out of the rod that Joseph held* it was not to just let it be known that he was the chosen one for Mary, but at that moment, he was given the grace of being immaculate to carry out this task.
We do not just have a Holy Family, we have an Immaculate One...
*Legend: in choosing a husband for Mary, among several suitors it was St. Joseph's rod that sprouted a lily and a dove rested on it.