Purpose: To develop a framework for simultaneous three-dimensional (3D) mapping of T-1, T-2, and fat signal fraction in the liver at 0.55T. Methods: The proposed sequence acquires four interleaved 3D volumes with a two-echo Dixon readout. T-1 and T-2 are encoded into each volume via preparation modules, and dictionary matching allows simultaneous estimation of T-1, T-2, and M0 for water and fat separately. 2D image navigators permit respiratory binning, and motion fields from nonrigid registration between bins are used in a non rigid respiratory-motion-corrected reconstruction, enabling 100% scan efficiency from a free-breathingacquisition.Theintegratednatureoftheframeworkensures the resulting maps are always co-registered. Results: T-1, T-2, and fat-signal-fraction measurements in phantoms correlated strongly (adjusted r(2) > 0.98) with reference measurements. Mean liver tissue parameter values in 10 healthy volunteers were 427 +/- 22, 47.7 +/- 3.3ms, and 7 +/- 2% for T-1, T-2, and fat signal fraction, giving biases of 71,-30.0 ms, and -5 percentage points, respectively, when compared to conventional methods. Conclusion: A novel sequence for comprehensive characterization of liver tissue at 0.55T was developed. The sequence provides co-registered 3D T-1, T-2, and fat-signal-fraction maps with full coverage of the liver, from a single nine-and-a-half-minute free-breathing scan. Further development is needed to achieve accurate proton-density fat fraction (PDFF) estimation in vivo.