When did the Church come up with the doctrine that each species (bread and wine) contains both the body and the blood of Christ?

Transubstantiation was officially defined in 1215 at the Fourth Lateran Council.

However, the Church has always held that “Christ is present whole and entire in each of the species and whole and entire in each of their parts” (CCC 1377).

The Council of Trent (1551) declared:

Because Christ our Redeemer said that it was truly his body that he was offering under the species of bread, it has always been the conviction of the Church of God, and this holy Council now declares again, that by the consecration of the bread and wine there takes place a change of the whole substance of the bread into the substance of the body of Christ our Lord and of the whole substance of the wine into the substance of his blood. This change the holy Catholic Church has fittingly and properly called transubstantiation. (Denzinger-Schönmetzer 1642)

According to the Catechism, “The Eucharistic presence of Christ begins at the moment of the consecration and endures as long as the Eucharistic species subsist. Christ is present whole and entire in each of the species and whole and entire in each of their parts, in such a way that the breaking of the bread does not divide Christ” (1377).