Conventional wideband beamformers are known highly sensitive to gain and phase errors in microphone characteristics, especially for small-sized arrays. Recently, a robust design approach for nearfield wideband beamformers using worst case performance optimization has been proposed. However, the worst case performance optimization criterion might be overly conservative in practice, which may lead to undesired low-pass filtered distortion of target signals. In this paper, a robust design approach for nearfield wideband beamformers using the worst case mean performance optimization is proposed, which is less conservative than the existing approach. Unlike the existing robust design approaches which have no control over array response variance, the presented approach further proposes to impose the passband response variance constraint to enhance the stability of passband array response and hence to reduce the target signal distortion. Moreover, some insights into the properties of array response variance are derived, which are helpful to better understand the robustness characteristics of nearfield wideband beamformers. Design examples demonstrate the effectiveness of the proposed robust design approach.