Measurement of the vibrations of plates can offer significant challenges to the experimentalist, particularly when the plates are lightweight, exhibit large amplitude deflections, nonlinear responses or are initially curved. The use of accelerometers adds masses which can change the dynamics of lightweight plates. Large amplitude oscillations and initial curvatures cause complications when using a laser vibrometer, as they make it difficult to get consistent reflections back to the receiver. Furthermore, large or nonlinear oscillations challenge inherent assumptions on which the vibrometer's algorithms depend. A high speed video camera avoids these issues, but makes it hard to extract numerical data. This paper describes a method that extends the capabilities of a high speed video camera by using a mirror, allowing post-processing software to stereoscopically resolve an array of points on the plate surface to 3D coordinates, capturing the complete shape and position of the plate throughout vibration. This method avoids all the problems mentioned above and gives very clear insight into plate vibration. Some example results of this method are presented, using thermally bistable carbon laminate plates filmed at a 1000 frames per second. These plates pose the challenges described, and also exhibit an unusual oscillatory motion where the plates 'snap' between two statically stable states. The method is shown to provide clear insight into the rich dynamics of these plates.