I am deployed to Afghanistan, and our current chaplain is a Church of Christ minister. In this situation would the Protestant service offered by the minister fulfill my Sunday obligation?
Attendance at a Protestant service does not fulfill the Sunday obligation. The Catechism instructs:
The first precept [of the Church] ("You shall attend Mass on Sundays and holy days of obligation and rest from servile labor") requires the faithful to sanctify the day commemorating the Resurrection of the Lord as well as the principal liturgical feasts . . . by participating in the eucharistic celebration, in which the Christian community is gathered (CCC 2042).
If participation in the celebration of the Eucharist is impossible, you have no obligation to attend Mass. But, in this situation:
It is specially recommended that the faithful take part in the Liturgy of the Word if it is celebrated in the parish church or in another sacred place according to the prescriptions of the diocesan bishop, or engage in prayer for an appropriate amount of time personally or in a family or, as occasion offers, in groups of families (Code of Canon Law 1248).