Poly(L-lactide) networks (PmLA) hydrophilized with different amounts of 2-hydroxyethyl acrylate (HEA) were investigated by dielectric relaxation spectroscopy, thermally stimulated depolarization currents, and differential scanning calorimetry. The incorporation of HEA units in the PmLA network, with the aim of modulating the water sorption capacity of the system, results in a material with a complex behavior. The system consists of phase-separated microdomains richer in one or the other comonomers that constitute the network. Initially, the addition of smalls amount of HEA units in the network gives rise to a one-phase, two-component system; however, when the amount of HEA in the system increases, a new phase (HEA-rich one) is formed containing some mLA chains that modify the main relaxation mode of these domains and the local dynamics of the system. The structure of the system has been analyzed by comparing the relaxational modes in the PmLA and PHEA homonetworks with those in the copolymer networks.