Local interstellar spectra (LIS) for protons, helium and antiprotons are built using the most recent experimental results combined with state-of-the-art models for propagation in the Galaxy and Heliosphere. Two propagation packages, GALPROP and HelMod, are combined to provide a single framework that is run to reproduce direct measurements of cosmic ray (CR) species at different modulation levels and at both polarities of the solar magnetic field. To do so in a self-consistent way, an iterative procedure was developed, where the GALPROP LIS output is fed into HelMod that provides modulated spectra for specific time periods of selected experiments to compare with the data. The parameters were tuned with a maximum likelihood procedure using an extensive data set of proton spectra from 1997-2015. The proposed LIS accommodate both the low energy interstellar CR spectra measured by Voyager 1 and the high energy observations by BESS, PAMELA, AMS-01, and AMS-02 made from the balloons and near-Earth payloads. The proton LIS also accounts for Ulysses counting rate features measured out of the ecliptic plane. The obtained solution is in a good agreement with proton, helium, and antiproton data by AMS-02, BESS, and PAMELA in the whole energy range.