This paper applies self-consistent field theory (SCFT) to discrete polymer chains consisting of a finite number of beads, N, joined together by freely jointed bonds of arbitrary potential, b(R). The numerics of this SCFT can be performed efficiently using spectral or pseudospectral algorithms, permitting its application to complex morphologies. To demonstrate its effectiveness, we examine diblock copolymer melts where the polymer bonds have a fixed length, a, and the nonbonded interactions have a finite range, sigma, with a strength controlled by the standard Flory-Huggins chi parameter. Although the results reduce to those of the usual SCFT for Gaussian chains in the limit of large N and small chi, there are some notable differences for short chains with strong interactions. The most significant involves the internal interfaces, which in turn affects the size of the domains. Furthermore, the finite range of the interactions, necessary to properly treat the internal interfaces, causes a noticeable shift of the ODT toward larger chi N. As chi becomes very large, particularly at small N, the finite extensibility of the freely jointed chains restricts the size of the domains, which leads to a preference for the lamellar phase.