the church is Israel?

The popular system of biblical interpretation in the church today is Dispensationalism, specifically Premillenial Pre-Tribulation theology. Popularized by Hal Lindsey in his 1970 book, Late Great Planet Earth (15 million copies sold), and recently with the Left Behind series by Tim F. LaHaye and Jerry B. Jenkins (also 15 million sold). I grew up with Dispensationalism and was never aware of any other view... until I discovered Reformed theology (trumpet sounds). Here's a brief summary of both systems:

DISPENSATIONAL THEOLOGY
Dispensationalism is a system of biblical interpretation formalized in the nineteenth century by John Nelson Darby and later popularized by the publishing of the study Bible of C. I. Scofield and the establishment of Dallas Theological Seminary by Lewis Sperry Chafer. It is the foundation of what is known in eschatological studies as "pre-tribulational premillenialism" and involves the division of history into (usually) seven distinct periods of time known as "dispensations". Twentieth century writers such as John Walvoord, Dwight Pentecost, and Charles Ryrie brought the doctrines of Dispensationalism into mainstream scholarship, which are often summarized by Ryrie's famous "sine qua non", i.e., his statement of the three primary tenets of the system. These are: 1) a clear distinction between Israel and the Church, 2) literal interpretation of Scripture, and 3) the glory of God as the primary goal of history.
- Christonomy.com

COVENANT THEOLOGY
Unlike Dispensationalism, Reformed (Covenant) Theology considers the seed of Abraham, the Israelites, to be part of the body of Christ. The Church did not replace Israel but organically springs out of the same root. God, from eternity, had merely planned, in the fullness of time, to expand His purpose, through Christ, to include other nations as well. All the spiritual seed of Abraham, Jew or Gentile are now one in Christ. Gentiles are a wild olive, grafted in among the Jews, the natural branches. Jesus "has made the two one and has destroyed the barrier, the dividing wall of hostility." Eph 2:12-14.
- Monergism.com

"This mystery is that through the gospel the Gentiles are heirs together with Israel, members together of one body, and sharers together in the promise in Christ Jesus. - Eph 3:6

Want to read more on this?
Monergism.com's section about Dispensationalism