The electrospinning technique combined with the electrospraying process provides a straightforward and versatile approach for the fabrication of novel nanofibrous biocomposite scaffolds with structural, mechanical, and biological properties potentially suitable for bone tissue regeneration. In this comparative investigation, three types of poly(3-hydroxybutyrate) (PHB)-based scaffolds were engineered: (i) PHB mats by electrospinning of a PHB solution, (ii) mats of PHB/hydroxyapatite nanoparticle (nHA) blends by electrospinning of a mixed solution containing PHB and nHAs, and (iii) mats constituted of PHB nanofibers and nHAs by simultaneous electrospinning of a PHB solution and electrospraying of a nHA dispersion. Scaffolds based on PHB/nHA blends displayed improved mechanical properties compared to those of neat PHB mats, due to the incorporation of nHAs within the fibers. The electrospinning/electrospraying approach afforded biocomposite scaffolds with lower mechanical properties, due to their higher porosity, but they displayed slightly better biological properties. In the latter case, the bioceramic, i.e. nHAs, largely covered the fiber surface, thus allowing for a direct exposure to cells. The 21 day-monitoring through the use of MTS assays and SEM analyses demonstrated that human mesenchymal stromal cells (hMSCs) remained viable on PHB/nHA biocomposite scaffolds and proliferated continuously until reaching confluence.