LED Circuit from a demo board -- not sure how both LEDs can function
Keep in mind that the B-C junction of a transistor will function like an ordinary diode when forward-biased. In normal transistor operation, this junction is usually reverse-biased.

When the Input is positive, the two transistors will regulate the current through the green LED such that the voltage drop across RLED2 equals the VBE of QLED2. 0.6V / 200&Omega; gives a current of about 3 mA, and this isn't particularly sensitive to the input voltage.

When the Input is negative, DLED3 is reverse-biased, so the current flows through RLED3, RLED2, the B-C junction of QLED2 and the B-C junction of QLED1 and then through the red LED. The current will depend on the voltage; an input voltage of about -12V will give the same 3 mA in the red LED.