We investigate a new scheme for astronomical spectrograph calibration using the laser frequency comb at the Solar Vacuum Tower Telescope on Tenerife. Our concept is based upon a single-mode fiber channel, that simultaneously feeds the spectrograph with comb light and sunlight. This yields nearly perfect spatial mode matching between the two sources. In combination with the absolute calibration provided by the frequency comb, this method enables extremely robust and accurate spectroscopic measurements. The performance of this scheme is compared to a sequence of alternating comb and sunlight, and to absorption lines from Earth's atmosphere. We also show how the method can be used for radial-velocity detection by measuring the well-explored 5 min oscillations averaged over the full solar disk. Our method is currently restricted to solar spectroscopy, but with further evolving fiber-injection techniques it could become an option even for faint astronomical targets.