This Letter demonstrates a method to simultaneously measure the quantitative-phase signal (QPS) of the observed specimen and the refractive index of its surrounding medium (n _m ) in a time-resolved manner using a micro-structured coverslip. Such coverslips, easily integrated into perfused live-cell imaging chambers, allow to use various quantitative-phase imaging techniques to achieve this dual measurement. Since QPS is crucially dependent on n _m , the measurement of the latter paves the way for its manipulation in a controlled manner leading to a QPS contrast modulation for appealing applications, including visualizing the interior of cells.