Visualizing chromatin adjacent to the nuclear envelope (denoted "epichromatin") by in vitro immunostaining with a bivalent nucleosome-binding antibody (termed monoclonal antibody PL2-6) has suggested a distinct and conserved chromatin structure. Moreover, different staining patterns for chromatin complexed with the monovalent "Fab" fragment of PL2-6, compared to the bivalent form, point to distinct binding interactions. To help interpret antibody/chromatin interactions and these differential binding modes, we incorporate coarse-grained PL2-6 antibody modeling into our mesoscale chromatin model and analyze interactions and fiber structures for the antibody/chromatin complexes in open and condensed chromatin, with and without linker histone H1 (LH). Despite minimal and transient interactions at physiological salt, we capture differential binding for monomer and dimer antibody forms to open fibers, with much more intense interactions in the bivalent antibody/chromatin complex. For these open "zigzag" fiber morphologies, differences result from antibody competition for peptide tail contacts with internal chromatin fiber components (nucleosome core and linker DNA). Antibody competition results in dramatic conformational and energetic differences among monovalent, bivalent, and free chromatin systems in the parental linker DNA / tail interactions. These differences in binding modes and changes in internal fiber structure, driven by conformational entropy gains, help interpret the differential staining patterns for the monovalent versus bivalent antibody/chromatin complexes. More generally, such dynamic interactions which depend on the complex internal structure and self-interactions of the chromatin fiber have broader implications to other systems that bind to chromatin, such as linker histones and remodeling proteins.