I do believe that hitting your children, even on the hand, shows them by example that it is OK to hit. They don't necessarily understand that the hitting is "different" because it is for discipline, or that they don't have the right to "discipline" you in the same fashion. They know that they did something that you didn't like, so you hit them. They assume that you do the right thing.
Likewise, I feel that biting your child is a bad idea. Haven't you ever heard the "he bit/hit me first!" argument going on between two children? They don't seem to remember who *actually* struck first, they just know that pretty soon, they are going back and forth; first one attacks, then the other, then the first "retaliates", which brings on retaliation from the other. Just because someone does something to you doesn't make it right to do it back to them.
The first response, about immediately picking up the child and putting them in Time Out, is IMO, the best option. This teaches your child that hurting others results in removal from others. No fun. Playtime stops. Believe me, Time Out works. I use it on both my boys - one is age 3 and one is almost 16. The 16 year old is considered one of the best behaved, politest, hardest working kids in our town, and is well loved by his teachers and friend's parents. My 3 year old is well on his way!