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We study the 3.4 − 4.4 μm fundamental rovibrational band of H₃⁺, a key tracer of the ionization of the molecular interstellar medium (ISM), in a sample of 12 local (d < 400 Mpc) (ultra)luminous infrared galaxies ((U)LIRGs) observed with JWST/NIRSpec. TheP,Q, andRbranches of the band are detected in 13 out of 20 analyzed regions within these (U)LIRGs, which increases the number of extragalactic H₃⁺detections by a factor of 6. For the first time in the ISM, the H₃⁺band is observed in emission; we detect this emission in three regions. In the remaining ten regions, the band is seen in absorption. The absorptions are produced toward the 3.4 − 4.4 μm hot dust continuum rather than toward the stellar continuum, indicating that they likely originate in clouds associated with the dust continuum source. The H₃⁺band is undetected in Seyfert-like (U)LIRGs where the mildly obscured X-ray radiation from the active galactic nuclei might limit the abundance of this molecule. For the detections, the H₃⁺abundances,N(H₃⁺)/N_H = (0.5 − 5.5)×10⁻⁷, imply relatively high ionization rates,ζ_H2, of between 3 × 10⁻¹⁶and > 4 × 10⁻¹⁵s⁻¹, which are likely associated with high-energy cosmic rays. In half of the targets, the absorptions are blueshifted by 50–180 km s⁻¹, which is lower than the molecular outflow velocities measured using other tracers such as OH 119 μm or rotational CO lines. This suggests that H₃⁺traces gas close to the outflow-launching sites before it has been fully accelerated. We used nonlocal thermodynamic equilibrium models to investigate the physical conditions of these clouds. In seven out of ten objects, the H₃⁺excitation is consistent with inelastic collisions with H₂in warm translucent molecular clouds (T_kin ∼ 250–500 K andn(H₂) ∼10^2 − 3cm⁻³). In three objects, dominant infrared pumping excitation is required to explain the absorptions from the (3,0) and (2,1) levels of H₃⁺detected for the first time in the ISM.