Low-lying multiphonon states in $^{136}\mathrm{Ba}$ have been populated with the inelastic neutron scattering reaction. Excitation functions were performed at neutron energies from 2.2 to 3.9 MeV, and $\ensuremath{\gamma}$-ray angular distributions were measured at 2.5, 3.0, and 3.5 MeV. Lifetimes have been determined using the Doppler-shift attenuation method, and electromagnetic transition rates have been deduced. The previously assigned ${2}_{1,\mathrm{ms}}^{+}$ mixed-symmetry state at 2128.9 keV has been confirmed and is not greatly fragmented. For the first time in the $N=80$ isotones, a ${3}_{2,\mathrm{ms}}^{+}$ two-phonon mixed-symmetry state is proposed. In addition, the ${2}_{5}^{+}$ and the ${4}_{3}^{+}$ levels at 2222.7 and 2356.4 keV, respectively, decay with large $B(M1)$ values to the two-phonon ${2}_{2}^{+}$ and ${4}_{1}^{+}$ states, respectively, which suggests two-phonon mixed-symmetric character. Their excitation energies, however, are not consistent with this interpretation.