We present for the first time to the best of our knowledge an all-fiber thulium (Tm) and erbium (Er) doped fiber laser simultaneously mode-locked by a common graphene saturable absorber. The laser consists of two ring resonators combined with a common saturable absorber (SA). The generated optical solitons have a full width at half maximum (FWHM) of 3.9 nm and 4.2 nm for Tm- and Er-doped laser, respectively. The used graphene layers were grown on copper foils by chemical vapor deposition (CVD) and transferred onto the fiber connector end. Broadband and flat absorption spectrum of used SA supports mode-locked operation at 1565 nm and 1944 nm. The repetition frequency of the resonator with Er-doped fiber was 20.19 MHz while the Tm-doped resonator was around 1 m longer and resulted with repetition rate of 18.43 MHz. The reported experiment unambiguously confirms one of the biggest advantage of the carbon nanomaterial (in this case graphene) SAs over semiconductor saturable absorption mirrors (SESAM), which is broadband operation range, allowing to mode-lock two lasers spectrally separated by almost 400 nm.