I've taken mine (03 HCH) to Jiffy Lube for the oil changes in-between the major tune ups (15, 30...). I've never had any problems. They don't carry 0W-20, but they carry 5W-20 which my owners manual says is an acceptable alternative. Funny thing - when I first bought the car I did the first 4-5 oil changes at the dealership - they didn't carry 0W-20 at the time either, and used 5W-20. They've always put my plate back on, but it's something I watch. I make sure they don't overfill either, which they've been prone to do with some other cars. However the Civic Hybrid is in their system and has all the specs. I've used them for the last 10 or so changes - no issues.

My Honda dealer puts in an addative every other oil change - not so sure if that's unique to the dealership or the Hybrid. Makes for a $50 oil change. I did it twice - didn't notice a change in mileage.