What is the Catholic Church's position on the relationship between science and religion? Hugh Ross in his book Navigating Genesis states that the "non-overlapping magesteria" model for the relationship between science and religion (of whom Stephen Jay Gould is a proponent) is endorsed by the Roman Catholic Church. 

He refers to Pope Pius XII's encyclical Humani Generis (1950) as evidence. 


Is the Catholic position indeed a separatist model? 
What is the current Catholic understanding of the relationship between science and religion? 


References to the Catechism of the Catholic church would be of valuable import, as well as any other official documents.
The "'non-overlapping magesteria' model for the relationship between science and religion" is not Catholic. In fact, it is condemned as a part of the heresy of Modernism, what Pope St. Pius X called the "synthesis of all heresies" in his 1907 encyclical condemning Modernism, Pascendi Dominici gregis (my emphases):Faith and Science

16. Having reached this point, Venerable Brethren, we have sufficient material in hand to enable us to see the relations which Modernists establish between faith and science, including history also under the name of science. And in the first place it is to be held [according to the Modernists] that the object of the one is quite extraneous to and separate from the object of the other. For faith [according to the Modernists] occupies itself solely with something which science declares to be unknowable for it. Hence [according to the Modernists] each has a separate field assigned to it: science is entirely concerned with the reality of phenomena, into which faith does not enter at all; faith on the contrary concerns itself with the divine reality which is entirely unknown to science. Thus the conclusion is reached that there can never be any dissension between faith and science, for if each keeps on its own ground they can never meet and therefore never be in contradiction. And if it be objected that in the visible world there are some things which appertain to faith, such as the human life of Christ, the Modernists reply by denying this. For though such things come within the category of phenomena, still in as far as they are lived by faith and in the way already described have been by faith transfigured and disfigured, they have been removed from the world of sense and translated to become material for the divine. Hence should it be further asked whether Christ has wrought real miracles, and made real prophecies, whether He rose truly from the dead and ascended into heaven, the answer of agnostic science will be in the negative and the answer of faith in the affirmative—yet there will not be, on that account, any conflict between them [according to the Modernists]. For it will be denied by the philosopher as philosopher, speaking to philosophers and considering Christ only in His historical reality; and it will be affirmed by the speaker, speaking to believers and considering the life of Christ as lived again by the faith and in the faith.

Faith Subject to Science

17. Yet, it would be a great mistake to suppose that, given these theories, one is authorised to believe that faith and science are independent of one another. On the side of science [according to the Modernists] the independence is indeed complete, but it is quite different with regard to faith, which is subject to science not on one but on three grounds [according to the Modernists:]


For in the first place it must be observed that in every religious fact, when you take away the divine reality and the experience of it which the believer possesses, everything else, and especially the religious formulas of it, belongs to the sphere of phenomena and therefore falls under the control of science. Let the believer leave the world if he will, but so long as he remains in it he must continue, whether he like it or not, to be subject to the laws, the observation, the judgments of science and of history.
Further, when it is said that God is the object of faith alone, the statement refers only to the divine reality not to the idea of God. The latter also is subject to science which while it philosophises in what is called the logical order soars also to the absolute and the ideal. It is therefore the right of philosophy and of science to form conclusions concerning the idea of God, to direct it in its evolution and to purify it of any extraneous elements which may become confused with it.
Finally, man does not suffer a dualism to exist in him, and the believer therefore feels within him an impelling need so to harmonise faith with science, that it may never oppose the general conception which science sets forth concerning the universe.


Thus it is evident [to the Modernists] that science is to be entirely independent of faith, while on the other hand, and notwithstanding that they are supposed to be strangers to each other, faith is made subject to science. All this, Venerable Brothers, is in formal opposition with the teachings of Our Predecessor, Pius IX, where he lays it down that: In matters of religion it is the duty of philosophy not to command but to serve, but not to prescribe what is to be believed but to embrace what is to be believed with reasonable obedience, not to scrutinise the depths of the mysteries of God but to venerate them devoutly and humbly.

The Modernists completely invert the parts, and to them may be applied the words of another Predecessor of Ours, Gregory IX., addressed to some theologians of his time: Some among you, inflated like bladders with the spirit of vanity strive by profane novelties to cross the boundaries fixed by the Fathers, twisting the sense of the heavenly pages…to the philosophical teaching of the rationalists, not for the profit of their hearer but to make a show of science…these, seduced by strange and eccentric doctrines, make the head of the tail and force the queen to serve the servant.

Pope Pius XII's 1950 encyclical Humani Generis was primarily about re-condemning Modernism in the form of the heretical "New Theology" that had sowed its rotten seed in seminaries and theological schools since Pope St. Pius X's time.