I went to a local pubmbing supply and they gave me the packing nut-stem-valve body sets for replacement. They do not carry both hot/cold, so I just get two identical ones.
The only differnce is, the new set I got comes with a O-ring seat in the valve body, which looks just like this one:
My old ones or the ones sold by the on-line supplier (attached Fig.) do not have that O-ring in the valve body.
I did not find any seat left in the bottom of the faucets either. (I peeked into the faucet with a flashlight)
So I hope the new ones will fit and work just well. Will see tonight.