The problem of two different pulses can be solved by using "Edge Triggered" Interupt. I don't know whether PIC16F84 has edge triggered interrupt pin. The uC is interrupted when it senses a transition from High level to Low Level or vice versa on this pin. This method is quite simple but has one drawback. For ex. consider that the interrupt is falling edge triggered, then on receiving a falling edge of positive pulse, it will start counting. Here, the counting is delayed by the amount of pulse duration since it has not started counting when the pulse went from 0 to 1 but it will start when it goes from 1 to 0. Similar delay will be observed when stopping the counter. But if the pulse is short, error will be very small.
For getting both pulses on same wire, you need to combine both the signals using "OR" gate.