What Diode have I here?
The diodes are SB540 schottky diodes.

If you look at the graph, in the link I posted, named: FIG. 3, you can see that the forward voltage of 0.16V is correct for the ammount of current through it: \$I=\frac{2.7}{3300}\approx 1mA\$.

And when you reverse the polarity of the voltage source, all of the voltage (if withing the maximum reverse voltage spec of the diode) should be across a working diode. So 2.7V across the diode when reverse-biased is expected.

You can do another faster/easier test to see if the diode is working. Do a continuity test on it. Most multimeters have this option on them (its a picture of a diode). So switch your multimeter to the continuity test and place the positive probe to the anode of the diode and negative probe to the cathode (side with the silver band) of the diode. If the multimeter shows some small value (some multimeters even beep) like 0.2V or similar and when you switch the probes and multimeter shows OL or value of 1, then the diode is a working one.