Chromatin domains formed in vivo are characterized by different types of 3D organization of interconnected nucleosomes and architectural proteins. Here, we quantitatively test a hypothesis that the similarities in the structure of chromatin fibers (which we call "structural homology") can affect their mutual electrostatic and protein-mediated bridging interactions. For example, highly repetitive DNA sequences in heterochromatic regions can position nucleosomes so that preferred inter-nucleosomal distances are preserved on the surfaces of neighboring fibers. On the contrary, the segments of chromatin fiber formed on unrelated DNA sequences have different geometrical parameters and lack structural complementarity pivotal for stable association and cohesion. Furthermore, specific functional elements such as insulator regions, transcription start and termination sites, and replication origins are characterized by strong nucleosome ordering that might induce structure-driven iterations of chromatin fibers. We propose that shape-specific protein-bridging interactions facilitate long-range pairing of chromatin fragments, while for closely-juxtaposed fibers electrostatic forces can in addition yield fine-tuned structure-specific recognition and pairing. These pairing effects can account for some features observed for mitotic and inter-phase chromatins.