Here, a novel protonable copolymer was realized for the production of polyplexes with a siRNA (inhibitor of STAT6 expression in asthma), with the aim of a pulmonary administration. The polycation was synthesized by derivatization of α,β-poly(N-2-hydroxyethyl)d,l-aspartamide (PHEA) with 1,2-Bis(3-aminopropylamino)ethane (bAPAE) in proper conditions to obtain a PHEA-g-bAPAE graft copolymer with a derivatization degree in amine (DDbAPAE%) equal to 35 mol%. The copolymer showed a proper buffering behavior, i.e., ranging between pH 5 and 7.4, to potentially give the endosomal escape of the obtained polycations. In effect, an in vitro experiment demonstrated the effect on biological membranes of the copolymer on bronchial epithelial cells (16-HBE) strongly dependent on the pH of the medium, i.e., higher at pH 5. bAPAE-based copolymers were further obtained with an increasing pegylation degree, i.e., equal to 1.9, 2.7, and 4.4 mol%, respectively. All the obtained copolymers were able to complex siRNA at a N/P ratio that decreases as the pegylation degree increases. At the same time, the tendency of polyplexes to aggregate and the capability to interact with mucin also decreases as the pegylation in the copolymer increases. Gene silencing experiments on 16-HBE showed that these copolymers have a significant role in improving the intracellular transport of naked siRNA, where the presence of PEG does not seem to hinder the cellular uptake of polyplexes. The latter obtained at polymer/siRNA weight ratio (R) equal to 10 with PHEA-g-PEG(C)-g-bAPAE also seems to be not susceptible to the presence of mucin, avoiding the polyanionic exchange of complexed siRNA, thus showing adequate behavior to be used as an effective vector for siRNA.