My mother comes from a long line of Eastern European/Russian Jews (and at least one Cohen). Her parents however were non-observant. She married a non-Jew and converted to Espiscopalianism. As I understand it, I then am considered Jewish since she was (even though I am not religious.) Is that right? I then married a non-Jew, and we did not raise our kids in any religion. What is the status of our children - simply "of Jewish descent"? (I am male)

One's Judaism is determined by the mother and there's no such thing as converting "out" of Judaism. Therefore, if your mother was born to a Jewish mother, than she was Jewish, and accordingly, you are just as Jewish as I am (regardless of whether one is religious or not, for Judaism is also a nationality, not just a religion). On the other hand, being that you are male and your wife isn't Jewish, your children are not Jewish at all, and as far as Judaism is concerned, there's no significance or standing to someone who just his father is Jewish.