Actually you are mistaken... even someone who is half jewish/half chinese will belong to the haplogroups of their parents. One maternal (mtDNA) and one paternal (Y-chromosome). You inherit your genes from both parents not just one.
Haplogroups cover large sections of the population for example Haplogroup J covers peoples from the Middle East, Turkey, Caucasus, Italy, Greece, the Balkans, North and Northeast Africa.
Even when you break Haplogroup J into smaller haplogroups (J*, J1 and J2) Each one covers massive segments of the population over several ethnic groups.
When you add Haplogroups from mtDNA you get an even more complex view of human relationships.
For example Haplogroup M1 includes people from Ethiopia and Somalia, through the Middle East and over to India and Haplogroup R is also found in a majority of people from the Middle East as well as West and East Eurasia. It is the the most common Haplogroup in Europe. And when you break down Haplogroup R you find the same deal as with Haplogroup J
People intermarry and otherwise "mingle" genetically since the dawn of time. As soon as Abraham married a woman his kids got both haplogroups from mom and dad.
The only way to have an "ethnically pure" haplogroup would be via profound inbreeding. Only if Abraham's sons married only Abraham's daughters would Abraham's lineage be a genetically pure one. It's basic genetics.