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Acoustic metasurfaces show non-traditional abilities in wave manipulation and provide alternate mechanisms for information communication and invisibility technology. However, most of the mechanisms remain narrow band (relative bandwidth ∼5%), and a wideband trait is essential for engineering applications. For example, controllable effective material properties—reflection or transmission phase—has barely been realized in wideband because the intrinsic dispersion relation is not always editable. In this paper, wideband reflection phase editing is realized, and wideband invisibility of a phase preserved Huygens's metasurface on a flat background is achieved with anomalous reflection. This metasurface is built with proposed unsymmetrical twin Helmholtz resonators which reach a predefined dispersion relation target value. The total instantaneous acoustic fields show nearly identical carpeting effects in a consecutive band with relative bandwidth 52.1% (from 5400 to 9200 Hz) in simulation and experiment. [ABSTRACT FROM AUTHOR]