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When protons and neutrons (nucleons) are bound into atomic nuclei, they are close enough together 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 structure and mapping out the strength and isospin structure (neutron-proton vs proton-proton pairs) of these virtual excitations is thus critical input for modeling a range of nuclear, particle, and astrophysics measurements. Hitherto measurements used two-nucleon knockout or ``triple-coincidence'' reactions to measure the relative contribution of np- and pp-SRCs by knocking out a proton from the SRC and detecting its partner nucleon (proton or neutron). These measurementsshow that SRCs are almost exclusively np pairs, but had limited statistics and required large model-dependent final-state interaction (FSI) corrections. We report on the first measurement using inclusive scattering from the mirror nuclei $^3$H and $^3$He to extract the np/pp ratio of SRCs in the A=3 system. We obtain a measure of the np/pp SRC ratio that is an order of magnitude more precise than previous experiments, and find a dramatic deviation from the near-total np dominance observed in heavy nuclei. This result implies an unexpected structure in the high-momentum wavefunction for $^3$He and $^3$H. Understanding these results will improve our understanding of the short-range part of the N-N interaction.