It really depends on who you are talking to. One Biewer club in the US says that they are a mixture. The other Biewer clubs and the German Kennel club where they came from says they are a purebred Yorkie - just with added color.
Parti Yorkies are a purebred tri-colored Yorkie that is recognized and can be registered with AKC. The Yorkie parent club (YTCA) does not recognize them and have made sure they can not be shown in AKC dog shows by making them a disqualifying color but AKC will recognize them as purebred (like white Boxers or white German Shepards).
There are several Parti Yorkie breeders on Yorkie Talk who can give you more information or you can do a search for the term Parti Yorkie to read previous discussions on this topic (they have gotten "heated" in the past).
Teresa