I found this question:
I want to convert to Judaism, but I am married to a Christian, Is this at all possible. […]
Most people would answer "no". I have heard countless times that this is the number one reason that you cannot convert. So first the Reform answer by Rabbi Debra Kassoff (relevant snippet only):
[…] So it is certainly possible, in the eyes of Reform Judaism, for you to convert. If you can convince a sponsoring rabbi that you are whole-hearted in your wish to convert to Judaism and that your current family and your new religious life can flourish together and support one another, then you will be well on your way. I wish you all the best.
So let’s move on to the relevant part of the Conservative answer by Rabbi Joel Rembaum (Emeritus):
[…] A married gentile may convert to Judaism even though the convert intends to remain married to the unconverted gentile spouse. Such conversion should take place, however, only after proper counseling and consultation assuring that the convert will be able to practice the Jewish religion without interference by the non-Jewish member of the family. Under these conditions, those who seek… ‘to shelter under the wings of the Shekhinah’ – … ‘may their numbers increase in Israel,’ … ‘and may blessings be bestowed upon them.’”
And finally a snippet from Orthodox answer by Rabbi David Feldman, Z”L
May one be converted to Judaism if the other spouse does not? The question has a straightforward answer: Yes, providing the proper circumstances accompany the response. […]
Maybe some expected a positive answer from a Reform rabbi (me not, as I have met people who told me otherwise), maybe a few even from a Conservative rabbi, but the Orthodox rabbi? Just wow! Thank you for returning my hope!