When protons and neutrons (nucleons) are bound into atomic nuclei, they are close enough to feel significant attraction, or repulsion, from the strong, short-distance part of the nucleon-nucleon interaction. These strong interactions lead to hard collisions between nucleons, generating pairs of highly energetic nucleons referred to as short-range correlations (SRCs). SRCs are an important but relatively poorly understood part of nuclear structure1-3, and mapping out the strength and the isospin structure (neutron-proton (np) versus proton-proton (pp) pairs) of these virtual excitations is thus critical input for modelling a range of nuclear, particle and astrophysics measurements3-5. Two-nucleon knockout or 'triple coincidence' reactions have been used to measure the relative contribution of np-SRCs and pp-SRCs by knocking out a proton from the SRC and detecting its partner nucleon (proton or neutron). These measurements6-8 have shown that SRCs are almost exclusively np pairs, but they had limited statistics and required large model-dependent final-state interaction corrections. Here we report on measurements using inclusive scattering from the mirror nuclei hydrogen-3 and helium-3 to extract the np/pp ratio of SRCs in systems with a mass number of three. We obtain a measure of the np/pp SRC ratio that is an order of magnitude more precise than previous experiments, and find a marked deviation from the near-total np dominance observed in heavy nuclei. This result implies an unexpected structure in the high-momentum wavefunction for hydrogen-3 and helium-3. Understanding these results will improve our understanding of the short-range part of the nucleon-nucleon interaction.