It would be very unhealthy for a 3 month old to sleep through the night, and I would run from any doctor who suggested it.
I recently read an article written by neurologists that discussed why babies wake during the night, and how it decreases their risk of sids and helps their brain develop. It is a necessary part of our biology to wake during the night when we are infants. It is only in our modern society that babies have been expected, and even forced to sleep through the night. One thing I would *not* do is try to give him food in order to help him sleep through the night. Not only is it bad for his intestines when he is so young (biologically, babies are supposed to have only breastmilk for the first 6 months + of life, and as much of it as they are willing), but at night, when his digestion is slowed down already, it is even worse for his system.
As far as sleep training and babywise goes, I would stay CLEAR away from those ridiculously cruel techniques enforced upon an innocent infant. If you do a search, many infants have died because their parents have followed the babywise series. It's BAD stuff. I would have to BEG you to stay away from that.... please don't let another sweet infant fall victim.
Our society needs to get out of the mindset that our babies need to learn to make our lives easier. They are infants... we are supposed to wake during the night with them, be exhausted for a while, love them with every ounce of our being, and do everything we can to help them develop into healthy adults. Forcing abnormal sleeping habits does not fall into this.
If your 3 month old is sleeping a 3 hour stretch, he is doing better than most! If the doctor asks how he's sleeping, just respond, "he sleeps like a baby!" --- because he does.
I will look up the studies from neurologists when I have a moment... have to run out the door in 30minutes.