A standard tandem triple-pass scanning Fabry-Perot interferometer of the Vernier type for applications in the near infrared is described. The Fabry-Perot etalons have been coated with a specially designed dielectric multilayer stack with low loss factors and a uniform reflectivity of (92.5 +/- 1.0)% between 730 and 860 nm. The performances of the instrument, such as resolution, total transmission, and contrast, are equivalent to conventional tandem Fabry-Perot spectrometers but over the whole near-infrared wavelength range. Applications of the system to Brillouin scattering on semiconductors in the transparent wavelength regime and high-resolution spectroscopy of vertical cavity surface-emitting lasers are given.