Background/Objectives: The development of polymer-lipid hybrid nanoparticles (PLNs) is a promising area of research, as it can help increase the stability of cationic lipid carriers. Hybrid PLNs are core-shell nanoparticle structures that combine the advantages of both polymer nanoparticles and liposomes, especially in terms of their physical stability and biocompatibility. Natural polymers such as polyhydroxyalkanoate (PHA) can be used as a matrix for the PLNs' preparation. Methods: In this study, we first obtained stable cationic hybrid PLNs using a cationic liposome (CL) composed of a polycationic lipid 2X3 (1,26-bis(cholest-5-en-3β-yloxycarbonylamino)-7,11,16,20-tetraazahexacosane tetrahydrochloride), helper lipid DOPE (1,2-dioleoyl-sn-glycero-3-phosphoethanolamine), and the hydrophobic polymer mcl-PHA, which was produced by the soil bacterium Pseudomonas helmantisensis P1. Results: The new polymer-lipid carriers effectively encapsulated and delivered model mRNA-eGFP (enhanced green fluorescent protein mRNA) to BHK-21 cells. We then evaluated the role of mcl-PHA in increasing the stability of cationic PLNs in ionic solutions using dynamic light scattering data, electrophoretic mobility, and transmission electron microscopy techniques. Conclusions: The results showed that increasing the concentration of PBS (phosphate buffered saline) led to a decrease in the stability of the CLs. At high concentrations of PBS, the CLs aggregate. In contrast, the presence of isotonic PBS did not result in the aggregation of PLNs, and the particles remained stable for 120 h when stored at +4 °C. The obtained results show that PLNs hold promise for further in vivo studies on nucleic acid delivery.