In this work, we report a synthetic approach to a Fmoc-protected nucleoamino acid, based on L-diaminopropanoic acid, carrying the DNA nucleobase on the alpha-amino group by means of an amide bond, suitable for the solid-phase synthesis of novel nucleopeptides of potential interest in biomedicine. After ESI-MS and NMR characterization this building block was used for the assembly of a thymine-functionalized nucleopeptide, composed of nucleobase-containing L-diaminopropanoic acid moieties and underivatized L-lysine residues alternated in the backbone. Circular dichroism studies performed on the cationic nucleopeptide and adenine-containing DNA and RNA molecules suggested that the thymine-containing peptide is able to interact with both DNA and RNA. In particular, a significant conformational variation in the RNA structure was suggested by CD studies. Human serum stability assays were also conducted on the cationic nucleopeptide, which was found to be highly resistant to enzymatic degradation.