Trent itself supposes both kinds of sin in the faithful
Thesis L. Finally, the chief reason Protestants judge the obedience believers give the law by Christ's grace to be imperfect is that it is constantly clouded by the sins of daily occurrence, which the papists call venial, and often interrupted by graver ones, which they call mortal. The councils of the Roman Church themselves, and Trent by name, acknowledge and presuppose both.
In session 6, chapter 11, Trent states that all people in this mortal life, however holy and righteous, fall at times into at least light and daily sins, the ones called venial. In canon 23 of the same session it anathematizes those who teach that a person once justified can avoid all sins, even venial ones, throughout his whole life, except by a special privilege from God.
In session 14, chapter 5, it approves and confirms the decree of the Lateran Council requiring each and every believer who has reached the age of discretion to confess his sins to a priest at least once a year, while the same council teaches in that chapter that venial sins need not be confessed, only mortal ones. Clearly, then, the council assumes that each and every believer does not usually get through a whole year without committing some grave sin that can be expiated only by solemn penance.
Latin
L. Denique cum obedientiam, quam fideles per Christi gratiam legi praestant, eo maxime nomine imperfectam esse censeant Protestantes, quod & quotidianae incursionis peccatis, quae venialia vocant Pontificii, assidue obscuretur, & gravioribus quoque, quae mortalia dicunt, non raro interrumpatur, utrumque hoc agnoscunt & supponunt ipsa Concilia Ecclesiae Romanae, & nominatim Tridentinum. Nam Sessione sexta, cap. undecimo, affirmat omnes in hac mortali vita, quantumvis sancti & justi sint, in levia saltem & quotidiana peccata, quae venialia dicuntur, quandoque cadere. Et in eadem Sessione Canone 23. anathema dicit eis qui docent hominem semel justificatum posse in tota vita omnia peccata, etiam venialia, vitare, nisi ex speciali Dei privilegio. Sessione vero 14. cap. 5. probat & confirmat constitutionem Concilii Lateranensis, per quam jubentur omnes & singuli fideles, posteaquam ad annos discretionis pervenerunt, saltem semel in anno, peccata sua confiteri sacerdoti: cum tamen idem Concilium, in eodem capite doceat non esse necessarium peccata venialia confiteri, sed mortalia tantum. Unde manifeste patet Concilium istud supponere omnes & singulos fideles, non solere annum integrum emetiri, quin grave aliquod peccatum admittant, quod non nisi per solennem poenitentiam expiari possit.