Not wanting to pay $70 for the coupler and AC adapter from Panasonic, I bought an aftermarket adapter/coupler from an Amazon seller.
Surprisingly, it works quite well! I was a bit worried that it might fry my GH2, but since the voltage is identical to the official adapter, there's no cause for concern.
Here's the link on Amazon. You can also find the same adapter for a couple bucks cheaper on eBay.

I've just ordered one based on your recommendation!

While on the subject of aftermarket products, has anyone tried this dual-charger which claims to be compatible with GH2 batteries?

Amazon.com: DUAL-ion+ DMW-BLC12 , DMW-BLD10 AC / DC Battery Charger For Panasonic DMC-G3 , DMC-GF2 , DMC-GH2 Cameras: Camera & Photo

I'd like to know if it charges to the same level (without overcharging) as the factory charger, how long it takes to charge compared to the factory charger, and whether the onscreen battery level displays properly after having charged a true Panasonic battery. So far, there's no reviews on the Amazon product page.

Thanks! I bought it and it works fine. :)