The signatures of the formation and evolution of a galaxy are imprinted in its stars. Their velocities, ages, and chemical compositions present major constraints on models of galaxy formation, and on various processes such as the gas inflows and outflows, the accretion of cold gas, radial migration, and the variability of star formation activity. Understanding the evolution of the Milky Way requires large observational datasets of stars via which these quantities can be determined accurately. This is the science driver of the 4MOST MIlky way Disc And BuLgE High-Resolution (4MIDABLE-HR) survey: to obtain high-resolution spectra at R ~ 20 000 and to provide detailed elemental abundances for large samples of stars in the Galactic disc and bulge. High data quality will allow us to provide accurate spectroscopic diagnostics of two million stellar spectra: precise radial velocities; rotation; abundances of many elements, including those that are currently only accessible in the optical, such as Li, s-, and r-process; and multi-epoch spectra for a sub-sample of stars. Synergies with complementary missions like Gaia and TESS will provide masses, stellar ages and multiplicity, forming a multi-dimensional dataset that will allow us to explore and constrain the origin and structure of the Milky Way.