Human and canine periodontium are often affected by an inflammatory pathology called periodontitis, which is associated with severe damages across tissues, namely, in the periodontal ligament, cementum, and alveolar bone. However, the therapies used in the routine dental practice, often consisting in a combination of different techniques, do not allow to fully restore the functionality of the periodontium. Tissue Engineering (TE) appears as a valuable alternative approach to regenerate periodontal defects, but for this purpose, it is essential to develop supportive biomaterial and stem cell sourcing/culturing methodologies that address the complexity of the various tissues affected by this condition. The main aim of this work was to study the in vitro functionality of a newly developed double-layer scaffold for periodontal TE. The scaffold design was based on a combination of a three-dimensional (3D) fiber mesh functionalized with silanol groups and a membrane, both made of a blend of starch and poly-ɛ-(caprolactone). Adipose-derived stem cells (canine adipose stem cells [cASCs]) were seeded and cultured onto such scaffolds, and the obtained constructs were evaluated in terms of cellular morphology, metabolic activity, and proliferation. The osteogenic potential of the fiber mesh layer functionalized with silanol groups was further assessed concerning the osteogenic differentiation of the seeded and cultured ASCs. The obtained results showed that the proposed double-layer scaffold supports the proliferation and selectively promotes the osteogenic differentiation of cASCs seeded onto the functionalized mesh. These findings suggest that the 3D structure and asymmetric composition of the scaffold in combination with stem cells may provide the basis for developing alternative therapies to treat periodontal defects more efficiently.