While the couple administers the sacrament, the priest is the Church’s official witness. They need to do this in front of him, or, in some cases, the deacon.
Now, the priest (along with the deacon and the bishop) is the ordinary minister of Holy Communion. Thus, it falls primarily to him to be the one distributing Holy Communion during the Mass, not the couple.
Please note what Redemptionis Sacramentum says:
[157.] If there is usually present a sufficient number of sacred ministers for the distribution of Holy Communion, extraordinary ministers of Holy Communion may not be appointed. Indeed, in such circumstances, those who may have already been appointed to this ministry should not exercise it. The practice of those Priests is reprobated who, even though present at the celebration, abstain from distributing Communion and hand this function over to laypersons.258
[158.] Indeed, the extraordinary minister of Holy Communion may administer Communion only when the Priest and Deacon are lacking, when the Priest is prevented by weakness or advanced age or some other genuine reason, or when the number of faithful coming to Communion is so great that the very celebration of Mass would be unduly prolonged.259 This, however, is to be understood in such a way that a brief prolongation, considering the circumstances and culture of the place, is not at all a sufficient reason.
Just out of curiousity, are you the one who is planning on getting married and wanting to distribute Holy Communion as well?