Dear Loretta,
Glory to Jesus Christ!
Sharon is right, and that the majority of Byzantine Funerals in America consist primarily in a celebration of the Divine Liturgy.
However, traditionally the actual funeral service is a kind of Matins service, at which hymns, canons, and litanies for the departed are sung. American practice is to incorporate some of this service into the Divine Liturgy.
But there are occasions where the older form still is celebrated, and some occasions when it must be celebrated. For example, there are certain "a-liturgical" days, when the Divine Liturgy may not be celebrated in the Byzantine Catholic Church. On these days, the funeral is taken alone without the Divine Liturgy. Or even I have heard of communion being given from the reserved mysteries as in the Liturgy of the Pre-Sanctified Gifts. Also on feasts, when the Festal Liturgy must be celebrated. It is not possible to combine aspects of the funeral Matins into a Feast Day Liturgy. In that case the older form of celebrating the Feast's Liturgy, and then at another time, the Funeral service without Liturgy is maintained.
As always, it seems liturgical questions in the Byzantine Church are complicated. But I wanted to indicate, that the funeral traditions do differ a little from the Roman Catholic tradition, where the "Funeral Mass" offered for the departed is the primary funeral service.
Elias, monk