<p>Axion-like particles (ALPs) arise from well-motivated extensions to the Standard Model and could account for dark matter. ALP dark matter would manifest as a field oscillating at an (as of yet) unknown frequency. The frequency depends linearly on the ALP mass and plausibly ranges from 10⁻²² to 10 eV/<i>c</i>². This motivates broadband search approaches. We report on a direct search for ALP dark matter with an interferometer composed of two atomic K-Rb-³He comagnetometers, one situated in Mainz, Germany, and the other in Kraków, Poland. We leverage the anticipated spatio-temporal coherence properties of the ALP field and probe all ALP-gradient-spin interactions covering a mass range of nine orders of magnitude. No significant evidence of an ALP signal is found. We thus place new upper limits on the ALP-neutron, ALP-proton and ALP-electron couplings reaching below <i>g</i>_{<i>a</i><i>N</i><i>N</i>} &lt; 10⁻⁹ GeV⁻¹, <i>g</i>_{<i>a</i><i>P</i><i>P</i>} &lt; 10⁻⁷ GeV⁻¹ and <i>g</i>_{<i>a</i><i>e</i><i>e</i>} &lt; 10⁻⁶ GeV⁻¹, respectively. These limits improve upon previous laboratory constraints for neutron and proton couplings by up to three orders of magnitude.</p>