One issue which I find puzzling is that many Reformed theologians claim that in Roman Catholicism, faith is defined as knowledge and assent, while Protestantism defines faith as including knowledge (notitia), assent (assensus) and trust (fiducia). Now that might be in interaction with Counter-Reformation apologist Robert Bellarmine, who is certainly a valid opponent and a premier scholar against the Reformation. But supposing that Bellarmine did in fact teach faith as consisting of mere assent, it only proves that at least a number of RC theologians taught thus. In practice, it does not seem to me that such is the case even in Tridentine Catholicism.
Consider the issue of implicit faith (fides implicita). In implicit faith, the parishioner is not required to have any knowledge whatsoever, but wholly assents and trusts that whatever the church says or teaches is true. We note here that there is indeed trust, but such is blind trust in the veracity of Rome, thus fiducia in ecclesia (trust in the church) and Sola Ecclesia (the Church alone). Furthermore, it is not as if Roman Catholics are called to merely trust the Roman Church, but rather they are called to trust in Christ, through the mediation of the Roman Church. Statement 154 of the Catechism of the Catholic Church states that Catholics are to be "trusting in God and cleaving to the truths he has revealed," thus showing forth that the assertion that Roman Catholicism denies fiducia is rather doubtful.
It seems therefore that in Roman Catholicism, faith is defined as assent and trust, with knowledge being optional. Now of course the claim can be made that what Protestant theologians mean by fiducia is different from what Rome means by trust, but that is really besides the point. The point is that Rome does in fact believe in fiducia- that one should place one's trust in God. That such trust is to be worked out through the mediation of Rome shows the difference between theirs and our understanding of trust, but it cannot be denied that they do embrace some version of the necessity of trusting in God.
In conclusion, it is best to not say that Roman Catholicism believes in faith as mere assent, but rather as blind assent. They do "trust" in God, but it is a God who is essentially unknown and made known only through Rome's mediation. Faith therefore in the Roman scheme has two parts: blind assent, and blind trust, and not mere intellectual assent.