Here's the thing about that. Some people think it's "racist" to view the Jews as a race, (notice the double speak? If Jews aren't a race, how can it be racist?).
However, ome ultra orthodox Jews DO view Jews as a race, and in Israel, immigration law allows any person who was born to a Jewish mother as a citizen of Israel if they are a believer or an atheist.
The issue of race or religion when it comes to the Jews is a difficult question, because unlike Christians, where there are Christians in Germany and Italy, yet those countries contain specifically Germans and Italians, Jews are not only everywhere in the world, but also share similar genetic traits despite living in different nationalities. You mention your parents were converts, so this probably does not apply to you.
I would say that Judaism is certainly a religion and that is what gives Jews their nationality, however, when you consider that this nationality has existed for thousands of years, and that historically Jews have intermarried with other Jews, it does create a type of selective breeding. This is perhaps why certain diseases are prevalent to Jewish people.
The other thing that complicates the issue is the Ashkenazi Jews who were historically Khazars who converted to Judaism in the 7th century AD. While they do not share the genetics of the Hebrew Semetic people, they are a definite race. In fact, most Jews alive today are Ashkenazi, usually the number is given as 90%. And when you get a DNA test to see if you are Jewish, the main two branches are Sephardic and Ashkenazi, Sephardic being the older, but smaller class of Jews.
So while people will probably call you an anti-semite for suggesting that the Jews are a race (even if you are Jewish), the fact remains that there are some indications of similar genetic traits. With that said, I believe everyone is an individual first, so it is really a moot point. I regard Jews as a religion, nationality, and race, but that does not mean I think they are better or worse than say, Spaniards or English.