Stimulated Brillouin scattering drives a coherent interaction between optical signals and acoustic phonons and can be used for storing optical information in acoustic waves. An important consideration arises when multiple optical frequencies are simultaneously employed in the Brillouin process: in this case, the acoustic phonons that are addressed by each optical wavelength can be separated by frequencies far smaller than the acoustic phonon linewidth, potentially leading to cross talk between the optical modes. Here we extend the concept of Brillouin-based light storage to multiple wavelength channels. We experimentally and theoretically show that the accumulated phase mismatch over the length of the spatially extended phonons allows each optical wavelength channel to address a distinct phonon mode, ensuring negligible cross talk and preserving the coherence, even if the phonons overlap in frequency. This phase-mismatch for broad-bandwidth pulses has far-reaching implications allowing dense wavelength multiplexing in Brillouin-based light storage, multifrequency Brillouin sensing and lasing, parallel microwave processing, and quantum photon-phonon interactions.