M.C.
This happened with my son too, he did pretty well until about 4 1/2 years old and then he started wetting the bed several times a week. I read on the web that it's entirely normal for kids up to age 6, so I stopped freaking out about it.
I use a great mattress pad (nice and thin but waterproof) but you still have to do laundry every day, so he and I (both) decided to use "good nights" or "underjams". We put them on over his underwear so he feels when he's wet (my husband was afraid if we put them on instead of underwear he wouldn't feel the wetness and wouldn't learn when he needed to go at night).
It works well and though you still have wet undies to deal with, you don't have to wash the sheets/pad every day. Also he can just get up and change out of the wet underjam himself and get back to sleep without having to change out the whole bed (your little guy would probably be too young to do that).
Like another poster said, some kids are just really heavy sleepers and can't get themselves up at night. And age 3 is really young (in my opinion) to be able to sleep all the way through without going to the bathroom - their bladders are just not big enough yet.
At that age I would have had no problem going back to pull ups until he seemed to stay dry through the night. If he's not bothered by using pull ups and you can handle the expense (remember, doing laundry every day is an expense too), it's worth it.
Lots of praise to the little guy when he does stay dry will help him too.
Good luck!