A growing body of work shows that the phase behavior of supramolecular polymers assembled from telechelic building blocks featuring binding motifs at the two termini is quite similar to that of conventional block copolymers. However, it remains unclear how crystallization of the phase formed by the binding motifs, which occurs in many supramolecular polymers, affects the phase morphology of such materials. Here we report a systematic investigation of a series of supramolecular polymers based on poly(ethylene-co-butylene) (PEB) telechelics and the complementary H-bonding pair isophthalic acid-pyridine (IPA-Py). These polymers were designed to feature two blocks that assemble into an amorphous low-glass-transition phase formed by the PEB segments and crystalline domains consisting of the binding motifs. The nature of the latter was systematically varied via the choice of the pyridine employed. The influence of the binding motif on the phase morphology and thereby properties of these supramolecular polymers was investigated by means of thermal analysis, polarized optical microscopy, (dynamic) mechanical analyses, small-angle X-ray scattering, and transmission electron microscopy. In the melted state, all materials assembled into hexagonal phases. However, when cooled below the crystallization temperature of the IPA-Py domains, three different scenarios were observed: breakout crystallization resulting in complex morphologies, retention of the melt morphology, and the formation of a lamellar phase.