The sensitivity of laser interferometers can be pushed into regimes that enable the direct observation of the quantum behaviour of mechanical oscillators. In the past, membranes with subwavelength thickness (thin films) have been proposed to be high-mechanical-quality, low-thermal-noise oscillators. Thin films from a homogeneous material, however, generally show considerable light transmission accompanied by heating due to light absorption, which potentially limits quantum opto-mechanical experiments, in particular at low temperatures. In this paper, we experimentally analyse a Michelson-Sagnac interferometer including a translucent silicon nitride (SiN) membrane with subwavelength thickness. We found that such an interferometer provides an operational point that is optimally suited for quantum opto-mechanical experiments with translucent oscillators. In the case of a balanced beam splitter of the interferometer, the membrane can be placed at a node of the electromagnetic field, which simultaneously provides lowest absorption and optimum laser noise rejection at the signal port. We compare the optical and mechanical models of our interferometer with experimental data and confirm that the SiN membrane can be coupled to a laser power of the order of 1Wat 1064 nm without significantly degrading the membrane's quality factor of the order of 106, at room temperature.