Does the Black Mesa mod for Half-Life 2 work with Episode 2? I couldn't find any clear answer on the mod page.
No. The Black Mesa mod is a high-def remake of Half Life 1. That's it. It uses the Source engine to do so; it's not a Half Life 2 mod, persay, as much as a total conversion. Half Life 2 was used as the starting point, but is not at all required to play Black Mesa.
What the mod page DOES say is:
Play for FREE! You need not purchase anything!, and classify it as a Half Life 2 mod. This conflicts, and the correct answer is the bullet point. Most likely, it was classified as a Half Life 2 mod because the database doesn't allow it to be blank. A better place to look is the official site.
HL2 also uses the Source engine, but is in no way required to play Black Mesa.
From this page
The only requirement to play Black Mesa is to have Source SDK Base 2007 installed on Steam. If you don't have it installed when you try to launch Black Mesa, Steam will download it for you
Also, according to the Half Life 2: Episode 2 Steam Page, the game "Includes Source SDK"
So yes, owning Half Life 2: Episode 2 (and ONLY that game) gives you access to Source SDK and thus, able to play the Black Mesa mod.