The perturbations imposed on benzene's S1(B-1(2u)) <-- S0(1A1g) vibronic transitions are studied in a series of mixed-solvent clusters of type C6H6-(H2O)n(CH3OH)m with (n+m) less-than-or-equal-to 4 using resonant two-photon ionization (R2PI) coupled with time-of-flight mass spectroscopy. The wide range of cluster types present in the expansion and the efficient fragmentation of the clusters following photoionization require the use of several probes beyond the mass-to-charge ratio to insure proper assignment of the major spectral features in the R2PI spectra. A selective loss of water over methanol from the mixed clusters is observed. A number of vibronic level features of the clusters, including the frequency shifts of absorptions, the cluster-induced S0-S1 origin intensity, the splitting of the degenerate v6 = 1 level in the S1 state. and the type and amount of intermolecular vibrational structure, are used to constrain the structures of the clusters in a general way. By comparison to previous studies of C6H6-(H2O)n and C6H6-(CH3OH)m clusters the following structural features for the BW(n)M(m) clusters are proposed as consistent with the experimental data: (1) BWM (B=benzene, W=water, M=methanol) appears to be composed of a water-methanol dimer bound on one side of benzene (analogous to the structures of BW2 and BM2). (2) BWM2 seems to incorporate a hydrogen-bonded WM2 chain much like BM3 While BW2M is composed of a cyclic hydrogen-bonded W2M much like BW3. (3) BW3M, BW2M2, and BWM3 are likely all cyclic structures whose spectral characteristics change smoothly with changing W/M ratio in the cluster. Finally, OPLS calculations are used to compare with the experimentally constrained structures and to address the relative energies of isomeric structures in the BW(n)M(m) clusters.