Your children will be considered as Jewish, as long as they have a Jewish upbringing and education. The Affirmations of Liberal Judaism state that children of mixed relationships, between a Jew and a non-Jew, are “considered Jewish if so brought up”.
Where the child is below seven-years-old, and will go on to have a Jewish upbringing and education, they are regarded as Jewish without need of conversion. The Liberal Beit Din (Rabbinic Board) will issue a status certificate, if required.
Where the child is over seven, Liberal Judaism would recommend attendance at religion school leading to bar/batmitzvah and Kabbalat Torah, at which point the child is considered fully Jewish. Again, a status certificate will be issued if required.
However, some people in this situation feel it helps establish their identity by applying to the Liberal Judaism Beit Din for a certificate of status.
For a fuller explanation on Jewish Status and Liberal Judaism’s principle of equilineal descent, you can read this in-depth article by Rabbi Alexandra Wright.
For the full Affirmation of Liberal Judaism on this topic, which contains a lot more detail and history, and covers many different scenarios, please click here.