What is Charon's ascending node in reference to?
I'm assuming this is Pluto's equatorial plane.


That is incorrect. Charon's right ascension of ascending node with respect to Pluto's equator is undefined. Seemingly paradoxically, it is well defined with respect to Earth's equatorial plane, and since that has become the universal plane of reference, that is what is used.



Charon and Pluto are tidally locked to one another. Their mean axes of rotation and orbital axes are identical. This means that Charon's orbit has zero mean inclination with respect to Pluto's mean equator, which in turn means that Charon's mean right ascension of ascending node with respect to Pluto's mean equator is undefined.

Charon's orbit about Pluto is however inclined with respect to the Earth's mean equator. In particular, it's inclined with respect to the Earth's mean equator at the J2000 epoch (noon Terrestrial Time on 1 Jan 2000). The Earth's mean equator at the J2000 epoch is the ICRF equator, to within a fraction of a milliarcsecond. The linked data clearly states that Charon's right ascension of ascending node is measured with respect to the ICRF equator.


Reference:

Brozović, Marina, et al. "The orbits and masses of satellites of Pluto." Icarus 246 (2015): 317-329.