We design single-wall carbon nanotube (SWNT) thin-film saturable absorbers (SAs) integrated onto semiconductor distributed Bragg reflectors for mode-locking solid-state Er:Yb:glass lasers. We characterize the low nonsaturable loss, high-damage-threshold SWNT SAs and verify their operation up to a pulse fluence of $2\mathrm{mJ}∕{\mathrm{cm}}^2$ . We demonstrate passive fundamental continuous-wave mode locking with and without group-delay dispersion compensation. Without compensation the laser produces chirped $1.8\mathrm{ps}$ pulses with a spectral width of $3.8\mathrm{nm}$ . With compensation, we obtain $261\mathrm{fs}$ Fourier-transform-limited pulses with a spectral width of $9.6\mathrm{nm}$ .