Interrupt fires a random number of multiple times for one pulse
Firstly, unless the processor pin is a Schmitt trigger, increasing capacitance will only make the problem worse by allowing any noise to be interpreted as multiple high-low transitions.  For a CMOS logic input the area around the transition point of 1/2 VDD typical is actually an area of linear operation, not digital. 

A Schmitt trigger introduces hysteresis such that when the signal is interpreted as a high level, it must go low by more than the hysteresis to be interpreted as a low level again.  This is accomplished with a bit of positive feedback added to a buffer where the output transition from low to high then pulls the input that much higher or a transition from high to low pulls the input that much lower:



The red line represents the typical CMOS threshold and the green lines represent the thresholds defined by the hysteresis of the Schmitt trigger.  The hysteresis defines the noise immunity of the input.  Most processors have pins that are equipped with a Schmitt trigger or and external device like a 74HC14 can be used.

Another way to deal with this type of noise is to lock out any transitions within the expected pulse-to-pulse transitions:  Once triggered, no more transitions are allowed until the lock out time expires.