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.