you didn't provide details (rise/fall time of input, impedances, levels ...) so this is a guess:

1) Fix your hardware using a Schmitt-trigger. 74HC14 or one of its single gate cousins.

2) Fix your hardware by software and 3 resistors. Using a software made Schmitt-trigger. IRQ routine switches an extra port pin which feeds back a resistor into the resistor network at the INT0 pin. You really have to know what you are doing otherwise this will work best on your laboratory desk.

3) Software only: INT0 IRQ does the routine you want it to handle; then masks itself; then enables a timer IRQ, then returns from IRQ. Timer IRQ in turn resets the INT0 Flag and reenables the INT0 IRQ. (If no free timer is available and baudrates are low you might be able to use the baudratetimer for the task).

Hope it helps
Frieder