In his excellent book on eschatology Cornelis Venema spends some time evaluating and critiquing dispensationalism from a Reformed and biblical perspective. Reformed theology is at odds with dispensationalism in several ways. One of the major differences is the understanding of promise/fulfillment and type/reality between the Old and New Testaments. There is much more to the discussion, of course, but here are a few helpful paragraphs of Venema to explain this difference.
“Perhaps the most telling evidence against the dispensationalistic hermeneutic is to be found in the book of Hebrews. The message of the book of Hebrews is, if I may speak anachronistically, a compelling rebuttal of Dispensationalism. Whereas the book of Hebrews is one sustained argument for the finality, richness, and completion of all the Lord’s covenant words and works in the new covenant that is in Christ, Dispensationalism wants to preserve the old arrangements intact for Israel, arrangements which will be reinstituted in the period of the millennial kingdom.
However, this would be tantamount to going back to what has been surpassed in the new covenant in Christ, reverting to arrangements that have been rendered obsolete and superfluous because their reality has been realized in the provisions of the new covenant. The Mediator of this new covenant, Christ, is the fulfillment of all the Lord’s promises to his people. Thus, to the writer to the Hebrews, any reversion to the old covenant types and ceremonies would be an unacceptable departure from the realities of the new covenant in preference for the shadows of the old.
Though it may seem too severe to some, no other judgment is permitted us respecting the system of biblical interpretation known as Dispensationalism: it represents a continued attachment to the shadows and ceremonies of the old covenant dispensation and also a failure to appreciate properly the finality of the new covenant. Its doctrine of a literal hermeneutic proves not to be literal in the proper sense of the term. Rather than reading the New Testament ‘according to the letter,’ Dispensationalism reads the New Testament through the lens of its insistence upon a radical separation between Israel and the church” (p. 294-5).