I am a Jewish convert and my fiancé is atheist (his family is not Jewish).
We found a rabbi willing to do a secular Jewish ceremony, and said he'd customize the ceremony to our needs/wishes. We plan on incorporating certain Jewish wedding traditions (a chuppah, signing a ketubah, breaking the glass), but we're not going to mention G-d especially in the vows.
(Our rabbi advised us to write our own vows.)
Our families are not expecting us to have a religious ceremony, or to have a certain kind of Jewish wedding, so that is not an issue.
I am curious how other couples have done secular Jewish ceremonies. I learned about Jewish wedding traditions during my conversion studies, but this will be my very first Jewish wedding.