Is faith reasonable? (Vatican I)

What is the relationship of reason and faith? 

The First Vatican Council answered this question in their Decrees. Session 3 (Dogmatic Constitution on the Catholic Faith), Chapter 3 (Of Faith and Reason) declares the following: 

There is a twofold order of knowledge, distinct both in principle and in object: in principle, because our knowledge in the one is by natural reason, and in the other by divine faith; in object, because, besides those things to which natural reason can attain, there are proposed to our belief mysteries hidden in God, which, unless divinely revealed, cannot be known.

 Reason can partially understand the mysteries of God, but it can’t understand them completely (as it can material things).  Still, there is no conflict: 

There can never be any real discrepancy between faith and reason; since the same God who reveals mysteries and infuses faith has bestowed the light of reason on the human mind, and God cannot deny Himself, nor can truth ever contradict truth.

 Moreover, 

they are of mutual aid one to the other: for right reason demonstrates the foundations of faith, and, enlightened by its light, cultivates the science of things divine; while faith frees and guards reason from errors, and furnishes it with manifold knowledge.

Richard John Neuhaus wrote the following about this document:

[It] corrected both the underestimation (in fideism and radical traditionalism) and the overestimation (in rationalism and ontologism) of reason’s natural capacities. Vatican I taught that faith and reason, revelation and the natural knowledge of God, are distinct but inseparable.  (From https://www.firstthings.com/article/1998/12/a-passion-for-truth-the-way-of-faith-and-reason)

 Thomas Joseph White wrote this summary:

[It] insisted, against secular reason, on the infallibility of divine revelation: Revelation is a gift that human rationality cannot procure for itself. Yet it also underscored the high natural capacities of human reason, our philosophical capacity to know of the existence of God and to cooperate with divine revelation. Against the reductive tendency of modern thought that so quickly rejects appeal to divine authority, that council sought to underscore the existence of a fruitful, liberating interaction between sacred theology and human rationality. The two are not at war, but may mutually interact with one another in peace and liveliness. Revelation is a gift to human reason seeking perspective. Reason seeking meaning can arrive at the threshold of the question of God and can therefore admit the possibility of divine revelation.  (From https://www.firstthings.com/article/2012/11/the-tridentine-genius-of-vatican-ii)