The masses of the lightest atomic nuclei and the electron mass1 are interlinked, and their values affect observables in atomic2, molecular3-5 and neutrino physics6, as well as metrology. The most precise values for these fundamental parameters come from Penning trap mass spectrometry, which achieves relative mass uncertainties of the order of 10-11. However, redundancy checks using data from different experiments reveal considerable inconsistencies in the masses of the proton, the deuteron and the helion (the nucleus of helium-3), suggesting that the uncertainty of these values may have been underestimated. Here we present results from absolute mass measurements of the deuteron and the HD+ molecular ion using 12C as a mass reference. Our value for the deuteron mass, 2.013553212535(17) atomic mass units, has better precision than the CODATA value7 by a factor of 2.4 and differs from it by 4.8 standard deviations. With a relative uncertainty of eight parts per trillion, this is the most precise mass value measured directly in atomic mass units. Furthermore, our measurement of the mass of the HD+ molecular ion, 3.021378241561(61) atomic mass units, not only allows a rigorous consistency check of our results for the masses of the deuteron (this work) and the proton8, but also establishes an additional link for the masses of tritium9 and helium-3 (ref. 10) to the atomic mass unit. Combined with a recent measurement of the deuteron-to-proton mass ratio11, the uncertainty of the reference value of the proton mass7 can be reduced by a factor of three.