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We investigate the lateral dynamics in a purely viscous lipid membrane which is supported by a thin polymer sheet (polymer-supported membrane). The generalized frequency-dependent mobility tensor of the polymer-supported membrane is obtained by taking into account the viscoelasticity of the polymer sheet. Due to its viscoelasticity, the cross-correlation functions of two particles embedded in the membrane exhibit an anomalous diffusion. A useful relation for two-point microrheology connecting the cross-correlation function and the modulus of the polymer sheet is provided.