Ba0.6Sr0.4TiO3/polyvinylidene fluoride (BST/PVDF) dielectric functional composites have been widely used in flexible wearable devices, capacitors, and energy storage devices. In addition to the ceramic phase type, polymer matrix type, composition, and interfacial connectivity of BST/PVDF composite materials, their morphology also significantly influences their electrical characteristics. Therefore, herein, sandwich-structured BST/PVDF layered composites were designed and prepared via tape-casting processing using different types of BST fillers [i.e., formless zero-dimensional (0D)-BST, rod-like one-dimensional (1D)-BST, and plate-like two-dimensional (2D)-BST]. The microstructures and electrical characteristics of sandwich-structured BST/PVDF composites were studied in relation to the BST morphology. The effects of the internal mechanisms of different interfacial models on the breakdown strength of BST/PVDF composites were discussed. According to our findings, unlike the 0D-BST and 1D-BST powders, 2D-BST powders form multiscale parallel interfaces in sandwich-structured composites due to their unique lamella-like morphology, which enhances the breakdown strength of sandwich-structured composites. Sandwich-structured BST/PVDF composites containing 2D-BST powders exhibit good electrical characteristics with an energy storage density of 19.71 J/cm3, an energy storage efficiency of 85.3%, a dielectric constant of 30.4 (1 kHz), a dielectric loss of 0.036 (1 kHz), and a dielectric tunability of 93.2%. This study provides a method for preparing functional composites with high dielectric tunability and high energy storage characteristics.