The application of ambient seismic noise cross‐correlation to distributed acoustic sensing (DAS) data recorded by subsurface fiber‐optic cables has revolutionized our ability to obtain high‐resolution seismic images of the shallow subsurface. However, passive surface‐wave imaging using DAS arrays is often restricted to Rayleigh‐wave imaging and 2D imaging along straight segments of DAS arrays due to the intrinsic sensitivity of DAS being limited to axial strain along the cable for the most common type of fiber. We develop the concept of estimating empirical surface waves from mixed‐sensor cross‐correlation of velocity noise recorded by three‐component seismometers and strain‐rate noise recorded by DAS arrays. Using conceptual arguments and synthetic tests, we demonstrate that these cross‐correlations converge to empirical surface‐wave axial strain response at the DAS arrays for virtual single step forces applied at the seismometers. Rotating the three orthogonal components of the seismometer to a tangential–radial–vertical reference frame with respect to each DAS channel permits separate analysis of Rayleigh waves and Love waves for a medium that is sufficiently close to 1D and isotropic. We also develop and validate expressions that facilitate the measurement of surface‐wave phase velocity on these noise cross‐correlations at far‐field distances using frequency–time analysis. These expressions can also be used for DAS surface‐wave records of active sources at local distances. We demonstrate the recovery of both Rayleigh waves and Love waves in noise cross‐correlations derived from a dark fiber DAS array in the Sacramento basin, northern California, and nearby permanent seismic stations at frequencies , up to distances of . The phase‐velocity dispersion measured on these noise cross‐correlations are consistent with those measured on traditional noise cross‐correlations for seismometer pairs. Our results extend the application of DAS to 3D ambient noise Rayleigh‐wave and Love‐wave tomography using seismometers surrounding a DAS array.