This concept is called concomitance. It was taught at the Council of Trent but does not originate at Trent. Trent was merely asserting Catholic belief against Protestant criticisms (e.g. Martin Luther who, in the Smalcald Articles, rejects both the doctrine of concomitance and the lawfulness of administering the sacrament under only one species). From the Council of Trent:
And this faith has ever been in the Church of God, that, immediately after the consecration, the veritable Body of our Lord, and His veritable Blood, together with His soul and divinity, are under the species of bread and wine; but the Body indeed under the species of bread, and the Blood under the species of wine, by the force of the words; but the body itself under the species of wine, and the blood under the species of bread, and the soul under both, by the force of that natural connexion and concomitancy whereby the parts of Christ our Lord, who hath now risen from the dead, to die no more, are united together; and the divinity, furthermore, on account of the admirable hypostatical union thereof with His body and soul. Wherefore it is most true, that as much is contained under either species as under both; for Christ whole and entire is under the species of bread, and under any part whatsoever of that species; likewise the whole (Christ) is under the species of wine, and under the parts thereof.
history.hanover.edu/texts/trent/ct13.html
The idea is not that the laity cannot receive both species, but that receiving either, one nevertheless receives the full Christ, “body, blood, soul and divinity.” Therefore, the Church may, for pastoral reasons, choose only to administer the species of bread to the congregation. This was the custom for a long time and is still the practice in many churches to this day, though I do not know the percentage. The reverse is sometimes true too. I see those with gluten intolerance take only the Sacred Blood. They are not receiving half of Christ, but the whole Christ.
That said, I would not rely on Craig for information about Catholicism. There was another thread a while back about Craig’s talks on Catholic beliefs of the Eucharist where it was showed that he was distorting Catholic teaching.
PS: I see that Joe beat me to it!