I loved my undergraduate years. I did my studies at the Moody Bible Institute and I cherish that school deep in my heart. I would still wholeheartedly recommend that school to anyone wishing to enter into vocational ministry especially if they see seminary in their future. That's because Moody is marked by a definitive love for God and his Word and it seeps into every aspect of campus life and studies at MBI. Also it's in the greatest city in the world; Chicago.
However, MBI is categorically not reformed and I knew that going in. That is because Moody holds to a dispensationalist theology. In fact, very many famous theologians held/hold this view (such as John MacArthur, Charles Ryrie, and of course D.L. Moody). Some people may know dispensationalism by it's fruits or results (such as the belief in there being two distinct peoples of God; Israel and the church). These fruits exist in this theological system because of what dispensationalism is at its core; a hermeneutical system.
Michael Glodo in the RTS faculty publication Covenant Theology gives a good brief description of the dispensationalist hermeneutic. He writes,
"In contrast to covenant theology, dispensationalism perceives a fundamental degree of discontinuity between the different periods of redemptive history (dispensations), not only between the Old and New Testaments but even between different epochs within each Testament."
It is because dispensationalism understands there to be discrete periods of time (dispensations) in God's dealings with the world. It is this discreteness that allows it to speak of there being more than one people of God. I also recall a Moody professor saying that the fourth commandment (concerning the sabbath) no longer applies to us because it wasn't reiterated in the New Testament like the others were.
Some more intense (and I would say more internally consistent) dispensationalists will speak of there being different modes of salvation throughout the dispensations. Where I have some serious concerns over such fruits as this Israel-church distinction, it is important to recognize that dispensationalism gets in the way of the Old Testament's entire organic nature and objective as well as the Christian's ability to "apply" the Old Testament.
The Case of the Proto-Gospel
Gen 3:15 is what is often referred to as the proto-gospel (or proto-euangelion for Greek geeks). This passage, found toward the end of the fall narrative, is a part of God's declaration after the guilt of Adam and Eve has been found out. Gen 3:15 reads,
"I will put enmity between you and the woman,
and between your offspring and her offspring;
he shall bruise your head,
and you shall bruise his heel"
This text is called the proto-gospel because it's the first revelation of a covenant of grace whereby God will rescue his people and consummate his perfect kingdom. It is the seed of revelation which will later fully bloom to the flower of Jesus Christ as the apex revelation (Heb 1:1-2). It is what kickstarts the rest of the Old Testament which beckons again and again the eventual coming messiah; Jesus Christ. Geerhardus Vos explains it better,
"In the mother promise, Gen 3:15, 'I will put enmity between you and this woman, and between your seed and her seed. It will crush your head and you will crush its heel.' Some have disputed that we are dealing with a covenant here. It must be conceded that the formal conclusion of a covenant is lacking, which, moreover, would have been incomprehensible to Adam and Eve. Only later, when the idea of a covenant had developed on natural terrain, God Himself used the term with Noah and Abraham, etc. But as far as the essence of the matter is concerned, the covenant was certainly with Adam since that mother promise. It was a protevangelium, a 'first gospel,' and the gospel is in itself a revelation of the covenant of grace."
This is a very significant fact! If Vos' covenant theology is correct (and I believe it is) then that means that throughout the entire Old Testament we will see building up, as if in anticipation, the eventual coming messiah who will fulfill all that is contained in the Old Testament itself. This means that the Old Testament has an objective that organically relates it to the New Testament... to present Christ crucified and raised (Luke 24:25-27). The Old Testament accommodated those believers in their redemptive-historical setting and the New Testament accommodates us in ours but they are organically related. Calvin illustrated this point in his Institutes,
"If a householder instructs, rules and guides his children one way in infancy, another way in youth, and still another way in young manhood, we shall not on this account call him fickle and say he abandons his purpose. Why then do we brand God with the mark of inconstancy because he has with apt and fitting marks distinguished a diversity of times"
This is where dispensationalism misses the mark. It sees the various epochs of history (redemptive history, that is) as more or less discrete. Whereas covenant theology, taking the lead of Scripture itself, sees the epochs of redemptive history as part of an organic whole. An organic whole which begins in a covenant of promise and hinges on the consummator of that covenant; Jesus Christ.
Of course this argumentation isn't in and of itself the final blow, as it were, to the dispensationalist hermeneutic. There are many more things to address. But it certainly a large issue that should be considered.