Okay...This is the definitive guide to tearing into your H3 rear axle. You can ignore most description pictures you run across...particularly for the Eaton kits. They use a generic photo, that doesn't even come close to the actual part you get. But trust me...the parts below fit your H3, and they are commonly needed anytime you want to do a rebuild. I've done a bunch of these and I have settled on the following list of manufacturers and part numbers. These can be bought from Summit, Jegs, Ebay, and Amazon. I occasionally buy direct from AAM (mostly for the front axle).
Eaton 8.6 GM 10b complete assembly #19659-010 (these only come in one offset 2.73 thru 5.38). The literature says this requires special carrier bearings but, that is for pre-99 vehicles, and doesn't apply to the H3.
Eaton Locking Mechanism Service Kit #29305-00S (this is the ramp plates & pin springs kit)
Eaton Gear & Pin Service Kit #29296-00S (this is the internal spider gears, side gears, cross shaft, and locking pins)
US Standard Gear 8.6 10b bearing kit #SPZ-58012 or
ZBKGM8.6 (this is a complete diff rebuild kit with bearings, pinion seal, crush sleave, pinion nut, and cover gasket)
DOES NOT FIT 09-UP!
US Standard Gear 8.6 10b bearing kit #SPZ-58013 or
ZBKGM8.6B (this is a complete diff rebuild kit with bearings, pinion seal, crush sleave, pinion nut, and cover gasket)
DOES NOT FIT 08-DOWN!
Timken rear axle shaft seal #TMK-4762N (this is seal on the end of the axle tubes)
EBC Greenie brake pads #EBC-DP61760
Wagner parking brake pads #Z908
MAX rear crossdrilled & slotted rotors #SY158222
Lube Locker re-usable 10-bolt cover gasket #LLR-G850
The US Standard bearing kits are what I normally use when rebuilding 8.6 axles. However, if you are doing a re-gear or a new locker install...you can buy "master" kits which come with ring gear bolts and shims for the pinion depth and backlash adjustments. Not all H3 rear axles are the same...2009 and 2010 models have a larger inner pinion bearing that requires a different kit.
Lastly...there are many small parts that can be bought direct from AAM if needed:
http://www.demandaam.com/axle-results?vm=GM&q=8.6"+10+Bolt+-+Rear+Axle