Computational studies of electrochemical interfaces based on density-functional theory (DFT) play an increasingly important role in the present research on electrochemical processes for energy conversion and storage. The homogeneous background method (HBM) offers a straightforward approach to charge the electrochemical system within DFT simulations, but it typically requires the specification of the active fraction of excess electrons based on a certain choice of the electrode-electrolyte boundary location, which can be difficult in the presence of electrode-surface adsorbates or explicit solvent molecules. In this work, we present a methodological advancement of the HBM, both facilitating and extending its applicability. The advanced version requires neither energy corrections nor the specification of the active fraction of excess electrons, providing a versatile and readily available method for the simulation of charged interfaces when adsorbates or explicit solvent molecules are present. Our computational DFT results for Pt(111), Au(111), and Li(100) metal electrodes in high-dielectric-constant solvents demonstrate an excellent agreement in the interfacial charging characteristics obtained from simulations with the advanced HBM in comparison with the (linearized) Poisson-Boltzmann model (PBM).