benefits of dual wielding?

Hello.

I am curious, when you dual wield, you alternate attacks.

Let's say, for example, you have this item: http://pathofexile.gamepedia.com/Al_Dhih
in your OFFHAND.

and let's say you swing a normal attack and you attack with the weapon in your MAINHAND.

Do you get the implicit and or explicit mods from the offhand weapon (e.g. the 8 life per hit or the 15% life leech)? Or is it only applied to that weapon when you hit with that weapon?

Thanks

EDIT: Here's another good example: http://pathofexile.gamepedia.com/Last_Resort

Do you get all those "on low life" mods to your main hand if you're low life? In particular, the increased attack speed is the questioning one.

Both the leech and life gain on hit are global, so they work for both your weapons.
Note that you don't alternate with all melee skills. Ground Slam, Double Strike and Leap Slam only use your main hand weapon. Any skill that requires a certain weapon type, like Glacial Hammer, Reave etc, still work and won't alternate if you have something else equipped in a hand.
I had a dual wield Ground Slam build that had Al Dhih on off hand for a while until Prismatic Eclipse was made.

Bump - could someone kindly address my edit in original post?

Thanks

@OP:

Yes, those buffs will apply to your main hand when on low life. You'll only get the damage boost, of course, if your main hand weapon is a claw.