I also was raised Greek Orthodox and am in a serious relationship with a Jewish man.We are really looking to see how we could have a future and family together, but there are not many available resources or people for us to talk to in a similar situation.
In the end, we were willing to let go of our respective religions, and cleaved together our own identity as a couple and family where faith takes a backseat to love. The next night we had a large Jewish wedding with a Rabbi at a private club. or Jewish services regularly, but have maintained a strong identity to each in the home through holiday observance.
My husband got baptized in a private ceremony for purposes of the ceremony, we had a small G. We had two boys; they’ve been brised and baptized, and they now go to Interfaith Sunday school. OUr boys will not be bar mitzvahed, a choice my husband made. These are the choice we’ve made, they are not perfect, but we are happy.
Not all christians are allowed to marry in the Greek Orthdox Church either: only those non-orthodox Christians that have been baptized in the name of the Trinity are allowed to marry.
And since an Orthdox Christian is not allowed to marry outside the Orthodox Church (whether in another christian church or civil/court ceremony), it doesn’t leave any options.
However I believe that in the Greek Orthodox Tradition your are considered to be a heretical Christian who is also a Jew.