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We report the discovery and characterization of two small transiting planets orbiting the bright M3.0V star TOI-1468 (LSPM J0106+1913), whose transit signals were detected in the photometric time series in three sectors of the TESS mission. We confirm the e planetary nature of both of them using precise radial velocity measurements from the CARMENES and MAROON-X spectrographs, and supplement them with ground-based transit photometry. A joint analysis of all these data reveals that the shorter-period planet, TOI-1468 b ($P_{\rm b}$ = 1.88 d), has a planetary mass of $M_{\rm b} = 3.21\pm0.24$ $M_{\oplus}$ and a radius of $R_{\rm b} =1.280^{+0.038}_{-0.039} R_{\oplus}$, resulting in a density of $ρ_{\rm b} = 8.39^{+ 1.05}_{- 0.92}$ g cm$^{-3}$, which is consistent with a mostly rocky composition. For the outer planet, TOI-1468 c ($P_{\rm c} = 15.53$ d), we derive a mass of $M_{\rm c} = 6.64^{+ 0.67}_{- 0.68}$ $M_{\oplus}$, a radius of $R_{\rm c} = 2.06\pm0.04\,R_{\oplus}$, and a bulk density of $ρ_{c} = 2.00^{+ 0.21}_{- 0.19}$ g cm$^{-3}$, which corresponds to a rocky core composition with a H/He gas envelope. These planets are located on opposite sides of the radius valley, making our system an interesting discovery as there are only a handful of other systems with the same properties. This discovery can further help determine a more precise location of the radius valley for small planets around M dwarfs and, therefore, shed more light on planet formation and evolution scenarios.