Christ is risen!
Perhaps my situation is a little less challenging than yours, but we are a "split" household, so to speak. I'm a cradle Byzantine Catholic, and my wife was raised as a Methodist (despite her father being Roman Catholic, and her mother originally Russian Orthodox - long stories, both ...).
Given my wife's Russian ethnic background on her mother's side, she connects well socially with our Church and our customs (she can put a very traditional basket together for Easter, and prides herself on her Pascha). Yet, even the other day (unsolicited), she said that she can never see herself converting. Her reasons are often those heard in opposition to the Roman Catholic line of thinking, what she likely hears in the media, and its challenging to try to overcome that bias.
Yet, we attend DL faithfully on Sundays and days of precept, and remain fully committed to raising our children as Byzantine Catholics, as we committed before marriage.
In that regard, we both remain bound to the family's Church, and I know of a few other families (including one where the husband is also a deacon in the Byzantine-Ruthenian Church) that are in similar situations.
What remains is a commitment to the children, and a mutual respect between the husband and wife, bound in marriage through Christ, and with Christ as the center of the marriage and family.
I still struggle to think of how I might be able to convince my wife, but she is strong willed and intelligent. In that regard, there is little difference between her and the many strong willed Eastern European women of my own family and ancestry.