Simply put, one who has not entered the life of the Church through Baptism, Chrismation, and the Eucharist—and who as such does not acknowledge Jesus Christ as his or her Lord, God and Savior—would reduce the Sacrament of Holy Matrimony to pure external form or ritual since he or she, by not acknowledging Jesus Christ, cannot properly seal his or her marriage in Him.In other words, marriage in Jesus Christ presumes that one accepts Him and believes in Him.
It is a matter of sacramentology, as well as common sense.
We raised our children in a home that observed all the major Jewish holidays.
I made our children aware of their culture and heritage.
In the Orthodox Church it is not permitted for an Orthodox Christian to be married to an individual who has not been baptized, regardless of whether they are of the Jewish, Muslim, Buddhist, or other faith.
While there is generally no exception to this rule, especially in the USA, you may wish to discuss your particular circumstance with your parish priest, who can offer specific guidance tailored to your individual situation.