If someone marries outside of the Church, he/she is not permitted to partake of the Holy Eucharist in the church even if he/she does not convert to a different denomination. All the Holy Sacraments are equal because all the Sacraments are a means of uniting with Christ through the Holy Spirit. Perhaps, some people trivialize Holy Matrimony as if it is just a ceremony, but in reality, it is a Holy Sacrament. If a marriage ceremony had taken place in a different church was out of ignorance, perhaps at a time when the couple did not know better, some provisions may be allowed thereafter. These situations are usually due to prior distancing from the church, and thus, the individuals may have lacked the sound spiritual knowledge of what is and is not acceptable according to the Church doctrine. Having said that, marriage is a Holy Mystery whereby two are joined and become one. It is an invisible Sacrament, but it is ever-existent. The union is spiritual, and one's spirit cannot be divided against itself. Worshiping with different belief systems cannot be reconciled. Indifference to either faith or denomination is also unacceptable and is certainly not the easy way out. Therefore, premarital counseling is actually mandated not only by the Coptic Orthodox Church, but the Catholic Church requires it as well.
The marital couple must be spiritually united and committed to pursuing a future with God as they strive toward their salvation together and make provisions to raise a godly family. The spiritual connectedness is severed when the two are partaking of Holy Communion through different means and with different preparations. There are many dogmatic differences between the Orthodox and the Catholic Churches. Even if either church allowed their own baptized individual to partake of Holy Communion in his/her church, it does not make sense that the other spouse will stand on the sidelines, a disconnected bystander, and a mere spectator.
The person who chooses to marry outside of the church stands to lose much and cuts him/herself off from the church. Consider the direction of the family and how and where the children's spiritual upbringing will develop. It is one thing to attend a different denominational school, so long as both parents are of the same faith and are united in the home with the same message regarding their faith to their children. Children of interfaith marriages will align their loyalties with one or the other parent and will become confused regarding the other church. They will not be able to accept both equally. That is a big risk to take and each parent will be held accountable for his/her decision affecting their children and their spiritual future.
I strongly advise a couple contemplating this serious decision to continue to thoroughly discuss the position of the Church with a Coptic Orthodox priest. Before making any rash emotional decisions, consider the great blessings that the young Moabitess widow, Ruth, received because she fully accepted the true faith of her husband. Even after his death, she willing remained wholeheartedly committed to the faith. The Lord rewarded her with a blessed family, her story is mentioned in a separate book in the Holy Bible ascribed to her by name, and Christ honored her by coming through her lineage. These words, she spoke to her mother-in-law:
"But Ruth said: 'Entreat me not to leave you, Or to turn back from following after you; For wherever you go, I will go; And wherever you lodge, I will lodge; Your people shall be my people, And your God, my God. Where you die, I will die, And there will I be buried. The LORD do so to me, and more also, If anything but death parts you and me.'" (Ruth 1:16-17).