This paper presents an analytical model to estimate the actuation potential of an electrostatic parylene-C diaphragm, processed on a glass wafer using standard microelectromechanical systems (MEMS) process technology, and integrable to polydimethylsiloxane (PDMS) based lab-on-a-chip systems to construct a normally-closed microvalve for flow manipulation. The accurate estimation of the pull-in voltage of the diaphragm is critical to preserve the feasibility of integration. Thus, we introduced an analytical model, in a good agreement with the finite element method (FEM), to extend the solution of the pull-in instability by including the effect of nonlinear stretching for multilayered circular diaphragms. We characterized the operation of fabricated diaphragms with a 300 mu m radius for the parameters, including pull-in voltage (221 V on average), opening and closing response times (in microseconds), repeatability (more than 50 times), and touch area (25.3% +/- 2.6% at pull-in potential). The experimental pull-in voltage shows close accuracy with the predicted results. Moreover, the diaphragm, sealed with a PDMS microchannel, was tested under fluid flow to prove the applicability of microfluidic integration. The hybrid fabrication method enables the realization of optically transparent and durable electrostatic microvalves for complex functioning of polymer-based microfluidic systems, as the extended analytical formulation permits accurate modeling of operation.