Fibrous scaffold along with seed cells are essential players for engineered tissue regeneration. Recently, PLGA/epoxidized poly(isoprene) dense membranes have been evaluated for cell growth and have shown satisfactory results. However, porous and fibrous structures suitable for obtaining 3D supports have not yet been evaluated for the PLGA/epoxidized poly(isoprene). The present work aimed to establish the electrospinning conditions for obtaining electrospun membranes with a smaller diameter of fibers and adequate morphology, which were characterized in vitro by their physical, chemical and biological properties. The best electrospun fibers were obtained from the following conditions: an applied voltage of 15 kV, a needle-collector distance of 20 cm and, a flow rate of 5 mL/h. The functional groups of the polymers involved in the blend did not show any changes. The mechanical properties of the electrospun membranes are within the lower limits known to human skin and some soft tissues. The in vitro degradation test showed a loss of mass of approximately 20% in 28 days. Significant adhesion and proliferation of human adipose–derived mesenchymal stem cells were demonstrated, indicating that there was cellular penetration into the scaffold and proliferation. Therefore, the preliminary results suggest that the electrospun PLGA/epoxidized poly(isoprene) membranes have high potential for application as a 3D tissue engineering scaffold.