We are not dispensationalists; all kinds of dispensationalism (anything that confuses Israel and the Church, or declares that the Church is not now fully Israel) are condemned as heresy by the Catholic Church. I believe the most common teaching is amillennialism, which is historically the most common teaching of all Christendom (East and West, Orthodox, Protestant, and Catholic), as it was taught by Augustine and Calvin as well; that is, the “millennium” is non-literal, and is the reign of Christ and the Saints in heaven, over the Church on earth - the “millennium” began, under this view, with the Session of Christ.
Postmillennialism is also rejected, as it believes that the Kingdom of God can be brought about through the exertions of man, coming dangerously close to the teaching of Pelagius writ large. It is very “evolutionary” in its teaching, that is to say, that man is on an endless march of secular-like “progress” from the lower to the higher, and by purely natural means will eventually become perfected along with his environment; and this will be the Kingdom of God. This is not to be confused with the “spiritual kingdom” of “the Kingdom of God is amongst you” or “the Kingdom of God is within you”, which are often used as proof-texts for the Postmillennialist view.
I am a historic premillennialist, as was taught in the teaching of St Irenaeus (that is, literal millennium after the second coming, with Christ ruling over earth directly). I’ve yet to receive a definitive answer whether this is considered heresy (in which case I would have to bring my mind in to conformity with the Church’s), or theologoumena or “allowable difference in theological opinion”. I’m also a six-day creationist (which is within the realm of theologoumena, even though many/most Catholics are progressive creationists and theistic evolutionists), so that may give you an inkling that I read the Bible a bit literally, believing that the other three Senses of Scripture are null and void if not founded on the literal-historical reading, or what is sometimes called the historico-grammatical hermeneutic (cf. St Basil’s Hexaemeron, St John Chrysostom’s Homilies on Genesis).
