Trent Part 1, Art IX
The Church militant is the society of all the faithful still dwelling on earth. It is called militant, because it wages eternal war with those implacable enemies, the world, the flesh and the devil.
The Members Of The Church Militant
The Church militant is composed of two classes of persons, the good and the bad, both professing the same faith and partaking of the same Sacraments, yet differing in their manner of life and morality.
The good are those who are linked together not only by the profession of the same faith, and the participation of the same Sacraments, but also by the spirit of grace and the bond of charity. Of these St. Paul says: The Lord knoweth who are his. Who they are that compose this class we also may remotely conjecture, but we can by no means pronounce with certainty. Hence Christ the Saviour does not speak of this portion of His Church when He refers us to the Church and commands us to hear and to obey her. As this part of the Church is unknown, how could we ascertain with certainty whose decision to recur to, whose authority to obey?
The Church, therefore, as the Scriptures and the writings of the Saints testify, includes within her fold the good and the bad; and it was in this sense that St. Paul spoke of one body and one spirit. Thus understood, the Church is known and is compared to a city built on a mountain, and visible from every side. As all must yield obedience to her authority, it is necessary that she may-be known by all.
That the Church is composed of the good and the bad we learn from many parables contained in the Gospel. Thus, the kingdom of heaven, that is, the Church militant, is compared to a net cast into the sea, to a field in which tares were sown with the good grain, to a threshing floor on which the grain is mixed up with the chaff, and also to ten virgins, some of whom were wise, and some foolish. And long before, we trace a figure and resemblance of this Church in the ark of Noah, which contained not only clean, but also unclean animals.
But although the Catholic faith uniformly and truly teaches that the good and the bad belong to the Church, yet the same faith declares that the condition of both is very different. The wicked are contained in the Church, as the chaff is mingled with the grain on the threshing floor, or as dead members sometimes remain attached to a living body.
Trent Part 1, Art IX