I am having a Bi-directional sensor switch with two cables, with single point ground. The way that the switch works is by changing the output voltage: 2.5V= standby, 0V=Pull, 5V=Push.
I want to handle the changes of the switch with interrupts, that's HIGH for push and LOW for pull. But since I have only one pin to use for interrupts (the other pin/cable is for ground), can I handle both interrupts on this one pin?
There is no need to use interrupts, and they won't work in this case.
With that sensor, you would use the analogRead() function to distinguish between true HIGH and LOW (a digital input on a 5V Arduino will treat 2.5V as LOW).
Hmmm. How is this 2.5 standby voltage achieved? This thread will go off the rails pretty quickly unless you clarify that by posting a lot more detailed information about the sensor. As presented, there is no way to interpret that signal without some special input circuitry to differentiate the different voltages, unless you take an analog reading as mentioned above. But it is possible that the sensor wiring offers another solution. Again, really need more info...
Also this talk of having only one pin for interrupts makes no sense. Please explain in more detail. One pin of what?
Without details of the sensor and/or a schematic, you will get no useful feedback.