This work describes the synthesis of poly(butylene adipate) (PBAd), by melt polycondensation, poly(l-lactic acid) (PLLA), by ring opening polymerization, and the new block copolymer PLLA/PBAd in ratios 90/10, 95/5, 75/25 and 50/50. Due to the biocompatibility and low toxicity of neat PBAd and PLLA, these copolymers are suitable to be used in biomedical applications. The 1H and 13C nuclear magnetic resonance spectroscopy techniques were employed for structural characterization. The thermal transitions, with an emphasis on crystallization, were assessed by differential scanning calorimetry, supplemented by X-ray diffraction and polarized optical microscopy. Molecular mobility studies were conducted using two advanced techniques, broadband dielectric spectroscopy and thermally stimulated depolarization currents. The results from the structural techniques, in combination with each other, provided proof of the presence of PLLA and PBAd blocks and, moreover, the successful copolymer synthesis. The overall data showed that the different co-polymer compositions result directly in severe changes in the polymer crystal distribution and, indirectly, the formation of PBAd micro/nano domains surrounded by PLLA. Furthermore, it was demonstrated that both the continuity of the two polymers throughout the copolymer volume and the semicrystalline morphology can be tuned to a wide extent. The latter makes these systems quite promising envisaging biomedical applications, including the encapsulation of small molecules, e.g. drug solutions. The molecular mobility map was constructed for these systems for the first time, revealing the local (short scale) and segmental (larger nm scale) mobility of PBAd and PLLA, as well as intermediate behaviors of the copolymers.