We utilize silicon-nitride waveguides to self-reference a telecom-wavelength fiber frequency comb through supercontinuum generation, using 11.3 mW of optical power incident on the chip. This is approximately 10 times lower than conventional approaches using nonlinear fibers and is enabled by low-loss (<2 dB) input coupling and the high nonlinearity of silicon nitride, which can provide two octaves of spectral broadening with incident energies of only 110 pJ. Following supercontinuum generation, self-referencing is accomplished by mixing 780-nm dispersive-wave light with the frequency-doubled output of the fiber laser. In addition, at higher optical powers, we demonstrate f-to-3f self-referencing directly from the waveguide output by the interference of simultaneous supercontinuum and third harmonic generation, without the use of an external doubling crystal or interferometer. These hybrid comb systems combine the performance of fiber-laser frequency combs with the high nonlinearity and compactness of photonic waveguides, and should lead to low-cost, fully stabilized frequency combs for portable and space-borne applications.