The evaluation of the properties and characteristics of macromolecular compounds is essential, especially from the point of view of the potential uses of the studied compounds. In this regard, poly(ethylene brassylate-co-squaric acid) (PEBSA) copolymacrolactone was investigated in order to correlate the relationships between the structure of the compounds and the generated properties. The study evaluates the physicochemical characteristics of PEBSA in interdependence with the ratio between comonomers, namely ethylene brassylate (EB) and squaric acid (SA), and the extent to which the structural tunability of the polymers generated by the SA content affects the properties in terms of the thermal stability, dielectric characteristics, and structural properties resulted from X-ray diffraction analysis. A good thermal stability of the copolymers was registered; this behaviour was interdependent with the squaric acid content and attributed to the intermolecular physical bonds achieved through the carbonyl functional groups of SA. The evaluation of the dielectric properties of the copolymers evidenced also the dependence of these characteristics on the SA content. The role of SA in creating self-organized morphologies with specific shapes and sizes was put into evidence by the AFM study. The supramolecular structure of PEBSA induced by the presence of squaric acid through hydrogen bonds interactions and π-stacking was confirmed by the X-ray diffraction. Also, both hydrogen donor and acceptor potential of these copolymers opens increased applicability for these new polymer systems.