Circuit to remove noise from digital communication line
Edit:

A low pass filter will ruin your nice square waves, but if all you want to do is trigger an interrupt, you can give one a try. Based on your new explanation I believe what you want is a low-pass filter where your cut-off is slightly above what is considered a valid bit which is:

1/(100 microseconds) = 10 kHz (valid bit)

I would select something like 12 kHz as your target cut-off and tweak from there.  Judging by the values you've chosen in your question, you will not achieve a cutoff frequency of interest.  Try the circuit in this example:



You can calculate your cutoff like so:

$$
f_{cutoff} = (\frac{1}{2*pi*RC})
$$

Some ball park values: R=68K and C=220pF will get you a cutoff of roughly 10.6 kHz.  This is a pretty poor filter and can be far improved, but give this a try and tell us if it attenuates those 30-40us pulses.  If it barely does anything (as I might suspect because this is first-order filter that attenuates 20dB/decade) then ask about second-order filters here.  You will get plenty of good answers.



Previous answer:

It seems that your receiver sensitivity is extremely high.  Can you share any more details on the transmitter, modulation, encoding, and receiving techniques?  You may have to tweak things there first.

This reminds me of a project I was involved in long ago (that also ended up winning an IEEE competition at our school :D) where we created a custom asynchronous protocol which sent pulses over a loosely coupled magnetic circuit which triggered a comparator and generated pulses similar to what you're seeing.  Since our baud rate was known on both ends, we ended up implementing a guard time on the receiving microcontroller and the transmission included a checksum as well.

Basically once we detected what we thought was a valid bit, we disabled the ISR for a period (corresponding to the baud rate of our transmission) before re-enabling it and accepting the next bit.  If the checksum didn't match we would throw it out and ask for a re-transmit.

We were operating in a very narrow band so we didn't get much noise, and we didn't have to deal with anything nearly as bad as what is depicted in your diagrams - If it had been that bad our technique probably would not have worked at all, or would have taken a very long time to send a valid transmission.  I would consider going over your front-end again and seeing if its ideal for what you want to accomplish.