The low-noise and phase-coherent nonlinear transformation of a narrowband laser into a broadband supercontinuum (SC) in an optical fiber forms the basis of extremely precise applications ranging from optical frequency comb technology to ultrafast photonics and biomedical imaging. A major challenge of this process is the avoidance of incoherent nonlinear effects that amplify random quantum noise, requiring careful birefringence and dispersion engineering of the fiber. However, fundamental trade-offs exist between working in normal or anomalous dispersion regimes. Here, we combine the benefits of nonlinear dynamics in both regimes by cascading soliton compression and optical wave breaking in a hybrid fiber, formed by joining two widely available, commercial, polarization-maintaining step-index fibers exhibiting anomalous and all-normal dispersion, respectively. We experimentally demonstrate that this hybrid approach results in an ultra-low-noise fiber SC source covering the 930–2130 nm range with phase coherence near unity, spectrally resolved relative intensity noise (RIN) as low as 0.05%, and averaging 0.1% over a bandwidth of 750 nm, approaching the theoretical limits close to the pump laser noise. This corresponds to a doubling of the generated spectral bandwidth and a decrease of RIN by up to 1 order of magnitude compared to direct pumping of the individual fibers, where modulational polarization instabilities play a limiting role. Owing to its simplicity and its scalability to high repetition rates, our hybrid scheme is readily applicable to various laser platforms and could enhance the performance of applications such as hyperspectral nonlinear microscopy, coherent optical communications, and photonic signal processing.