This study employed density functional theory with doubly screened dielectric-dependent hybrid (DSH) functional to predict the band gaps of Pb- and Sn-based inorganic and hybrid 3D halide perovskites, as well as layered hybrid perovskites. The DSH functional employs material-dependent mixing parameters derived from macroscopic electronic dielectric constant, and accurately predicts band gaps for 3D perovskites only if structural local disorder is taken into account. For layered hybrid perovskites, we propose using the calculated dielectric constant of the respective 3D perovskites to define the DSH screening. This dataset contains input and output files of all DFT and DSH calculations applied to Pb- and Sn-based layered halide perovskites with various organic spacers and multilayered structures, such as BA series with n =1, 2, 3. The computational framework introduced here provides an efficient parameter-free ab initio methodology suitable for predicting the electronic properties of 3D, layered halide perovskites and their heterostructures, towards modelling materials for advanced optoelectronic devices.