Polymer self-assembly plays a critical role in a range of soft-material applications and in the organization of chromosomal DNA in living cells. In many cases, the polymer chains are composed of incompatible monomers that are not regularly arranged along the chains. The resulting phase segregation exhibits considerable heterogeneity in the microstructures, and the size scale of these morphologies can be comparable to the statistical correlation that arises from the molecular rigidity of the polymer chains. To establish a predictive understanding of these effects, molecular models must retain sufficient detail to capture molecular elasticity and sequence heterogeneity. This talk highlights efforts to capture these effects using analytical theory and computational modeling. First, we demonstrate the impact of structural rigidity on the phase segregation of copolymer chain in the melt phase, resulting in non-universal phase phenomena due to the interplay of concentration fluctuations and structural correlation. We then demonstrate how these effects impact the phase behavior in statistical random copolymers and in heterogeneous copolymers based on chromosomal DNA properties. With these results, we demonstrate that the spatial segregation of DNA in living cells can be predicted using a heterogeneous copolymer model of microphase segregation.