When was the atmosphere of Venus first observed? Nowadays, atmospheres of transiting exoplanets are being characterized. We can measure the absorption of the star's light through the exosphere of exoplanets. 

The same can be done closer to Earth, with the inner planets. In fact, this was done during the 2012 Venus transit. 

When is the first time that a transit was used to study the atmosphere of Venus ?
The discovery is attributed to Mikhail Lomonosov, who inferred the presence of the Venusian atmosphere from observations of the transit of Venus in 1761, although this has been challenged by Pasachoff &amp; Sheehan (2012) who argue that Lomonosov's observations do not match the phenomena observed during the 2004 transit, arguing that Lomonosov's telescope was not capable of detecting the Venusian atmosphere. They suggest that the strongest claim for detecting the atmosphere was by David Rittenhouse who observed the 1769 transit, although they assign the greatest credit to Johann Schröter (1796) who also took into account out-of-transit observations of the ring of light around the planet at inferior conjunction.

This challenge was itself challenged by Koukarine et al. (2013) who observed the 2012 transit of Venus using antique refractors, concluding that Lomonosov's experimental procedure was sufficient to detect the atmosphere and support the attribution of the discovery to Lomonosov.

An in-depth summary can be found in a review article by Vladimir Shiltsev in the Journal of Astronomical History and Heritage (2014).