Thanks for the replies. It helped with pointing me in the right direction to start looking.
I found that with a 10k pullup, some of the pulses from the input where still present on the output, even when the device was in the "off state". The pulses where reduced with a 1k pullup, but still present at the output of the buffer.
I agree, 10nF is likely too much capacitance, but it's what I had handy at the time to test.
After some more reading, I understand that there is a this part is a solid state relay, slightly different from an octocoupler.
Ultimately, I would like to implement a SPDT switch using SPST solid state relays. I would like to see a good app note/reference design on how to do this, especially with reference on where pullups/pulldowns are required for using solid state (as opposed to electromechancial) devices.