The assurance and confirmation found in the Lord's Supper...

The divine and the human nature have this personal union with each other in the person of Christ and have the communion resulting from it (in deed and truth).  For this reason, there is attributed to Christ (according to the flesh) what His flesh, according to its nature and essence, cannot be by itself.  Apart from this union, His flesh cannot have these attributes:  His flesh is a truly live-giving food and His blood a truly life-giving drink.  The two hundred Fathers of the Council of Ephesus have testified that Christ's flesh is a life-giving flesh.  Therefore, this man only, and no man besides, either in heaven or on earth, can say with truth, "Where two or three are gathered in My name, there am I among them" (Matthew 18:20).  Also, "And behold, I am with you always, to the end of the age" (Matthew 28:20).

We do not understand these testimonies to mean that only Christ's divinity is present with us in the Christian Church and Congregation, and that such presence does not apply to Christ according to His humanity in no way whatever.  For in that way Peter, Paul, and all the saints in heaven—since divinity, which is everywhere present, dwells in them—would also be with us on earth.  However, the Holy Scriptures say this only about Christ, and no other man.  We hold that by these words the majesty of the man Christ is declared.  Christ as receive this majesty, according to His humanity, at the right hand of God's majesty and power.  So also, according to His receive human nature and with the same, He can be, and also is, present where He wants to be.  He is present especially in His Church and congregation on earth as Mediator, Head, King, and High Priest.  This presence is not a part, or only one half of Him.  Christ's entire person is present, to which both natures along, the divine and the human—not only according to His divinity, but also according to, and with, His received human nature.  He is our Brother, and we are flesh of His flesh and bone of His bone.  He has instituted His Holy Supper for the certain assurance and confirmation of this, so that He will be with us, and dwell, work, and be effective in us also according to that nature from which He has flesh and blood.
~BOC, FSD, VIII, 76-79

Christ fulfills His office in, according do, with, and through both natures...

In fulfilling Christ's office, the person does not act and work in, with, through, or according to only one nature.  It works in, according to, with, and through both natures.  As the Council of Chalcedon expresses it, one nature works in communion with the other what is a property of each.  Therefore, Christ is our Mediator, Redeemer, King, High Priest, Head, Shepherd, and so on, not according to one nature only (whether it be the divine or the human), but according to both natures.
~BOC, FSD, VIII, 46-47