Hebrews are a race, not Jews. That was Adolf Hitler's major mistake when he tried to eradicate the "race" of Jews--his quest was impossible since Jews belong to a religious group. Jews are an ethnic group because there are converts to Judaism that can keep the tradition going even if the race of Hebrews eventually die out.
I do not think that the Jewish people are a race. They are an ethnic group. A race refers to a group of people that are defined by their genetic differences. The Jewish are a group of people that is mainly defined by the religion to which they follow and have a faith in.
I think Jewish people are more of an ethnic group based on how they are formed. However, they do share the same characteristics as a race. They are a group of people with the same beliefs and have common ancestors, social groups, language and they all are striving for the same rights.
I would go as far as to say neither answer is wrong, but I think of the Jewish people as an ethnic group. Amongst this ethnic group it is possible that there are several races being accounted for, and I think this is the key distinction for telling the two apart.
No, I do not believe that the Jewish people are a race, because it is something that is passed down by blood line. A person is Jewish regardless of what color they are, if they have a parent or other ancestor that is a Jewish person. They are also distinguished by their beliefs.