Several composites based on poly(3-hydroxybutyrate) (PHB) and mesoporous SBA-15 silica were prepared by solvent-casting followed by a further stage of compression molding. The thermal stability, phase transitions and crystalline details of these composites were studied, paying special attention to the confinement of the PHB polymeric chains into the mesopores of the silica. For that, differential scanning calorimetry (DSC) and real-time variable-temperature X-ray scattering at small angles (SAXS) were performed. Confinement was stated first by the existence of a small endotherm at temperatures around 20 °C below the main melting or crystallization peak, being later confirmed by a notable discontinuity in the intensity of the main (100) diffraction from the mesoporous silica observed through SAXS experiments, which is related to the change in the scattering contrast before and after the crystallization or melting of the polymer chains. Furthermore, the usual α modification of PHB was developed in all samples. Finally, a preliminary investigation of mechanical and relaxation parameters was carried out through dynamic–mechanical thermal analysis (DMTA). The results show, in the temperature interval analyzed, two relaxations, named α and β (the latest related to the glass transition) in order of decreasing temperatures, in all specimens. The role of silica as a filler is mainly observed at temperatures higher than the glass transition. In such cases, stiffness is dependent on SBA-15 content.