The strongest sections of this book, not surprisingly, are those that deal with human races generally. Corcos would go so far as to replace the term race with "deme," denoting "groupings." "No matter how many [racial] groups we propose, we always find people who do not fit any one category. Racial classification is impossible because humanity is very diverse, and distinct lines of demarcation among groups do not exist."
So races do not exist (in the biological sense). Social convention may make us group people as one "grouping" or another, but that is a whole different thing.
Nazi policies labeled centuries-long residents in German territory who were not ethnic Germans such as Jews (understood in Nazi racial theory as a "Semitic" people of Levantine origins), Romanis (also known as Gypsies, an "Indo-Aryan" people of Indian Subcontinent origins), along with the vast majority of Slavs (mainly ethnic Poles, Serbs, Russians etc.), and most non-Europeans as inferior non-Aryan subhumans (i.e. non-Nordics, under the Nazi appropriation of the term "Aryan") in a racial hierarchy that placed the Herrenvolk ("master race") of the Volksgemeinschaft ("people's community") at the top
Ok, here the sources is Wikipedia, which I admit is of low quality. However this paragraph is pretty well anotated. The sources are legit.
Final link. Genetic markers cannot determine Jewish decent. I think that says it all.
So what are we left with: Races as understood in the first post above in this thread, can only be understood as being cultural. Thus it is rather strange to call somebody a half-jew. Especially if he/she doesn't practice the cultural definitions of his/her "race".