When talking to a native German speaker, should I refer to Christmas Eve as "der Heilige Abend" or "der Heiligabend" or are either appropriate?
I am a native speaker living in Vienna, Austria, and »Heiligabend« sounds very strange to me. I hear it very often in German TV, and I have have friends who grew up in Germany who also say »Heiligabend«, but nobody who grew up here in Austria uses this word. We always say »Heiliger Abend«. Also in Austrian TV you will always hear »Heiliger Abend«.
So, the answer is: Both terms are correct, but »Heiligabend« seems to be more common in northern parts of German language area, while in southern parts »Heiliger Abend« is used much more frequently.
"Heiligabend" is the term for Christmas Eve in German. It's like "Ostersonntag" or "Karfreitag".
The term "heiliger Abend", however, can also be used and will be understood, as there's only one of them :-) It will especially be used in southern regions of Germany when declinated. While in northern Germany one would say "An Heiligabend gehen wir in die Kirche", in southern Germany you'd say "Am heiligen Abend gehen wir in die Kirche".