From the LCMS website:
QUESTION: What verses in Scripture can be cited that teach “that BOTH bread and wine AND Christ’s true body and blood” are present in the Lord’s Supper?
ANSWER: All three accounts of the institution of the Lord’s Supper in the Gospels (Matt. 26:26-29; Mark 14:22-25; Luke 22:14-23) explicitly state that Jesus took BREAD, blessed it, broke it, and gave it to his disciples saying, “Take, eat; this [i.e., this BREAD, which I have just blessed and broken and am now giving to you] is my body.”
Jesus uses similar language in referring to “the cup” (of wine) as “His blood.” A plain and straightforward reading of these words leads to the conclusion that BOTH bread AND body, BOTH wine AND blood are present in the consecrated elements of the Lord’s Supper.
Perhaps the most explicit expression of this truth, however, is found in 1 Cor. 10:16-17, where Paul writes:
“The cup of blessing that we bless, is it not a participation in the blood of Christ? The bread that we break, is it not a participation in the body of Christ? Because there is one bread, we who are many are one body, for we all partake of the one bread.”
Paul clearly says here that we all “partake” of “BREAD” when we receive the Lord’s Supper—even as we also partake of and “participate in” the true body of Christ. And he says we all “partake” of the wine (the cup), even as we also partake of the true blood of Christ.
Similarly, in 1 Cor. 11:26, Paul says: “For as often as you eat this bread and drink the cup, you proclaim the Lord’s death until he comes.”
Paul expressly states here that when we receive the Lord’s Supper we are “eating bread” and “drinking the cup” (wine), but he goes on to say those who eat this bread and drink this cup are also partaking of the true body and blood of Christ.
So “real” is this participation in Christ’s body and blood, in fact, that (according to Paul) those who partake of the bread and wine “in an unworthy manner” are actually guilty of “profaning the body and blood of the Lord” (1 Cor. 11:27).
(Partaking of the Lord’s Supper “in a worthy manner,” of course, is not something that we “do” or “accomplish” on the basis of our “personal holiness” or “good works.” It means receiving God’s free and gracious gifts of life and forgiveness offered in the Lord’s Supper in true repentance produced by the work of the Spirit through God’s Law and in true faith in Christ and His promises produced by God’s Spirit through the Gospel).