I agree with your hubby that teaching him tunes is a great idea. My daughter, barely four, sounds like yours: her attention span is very short. But, I've still been able to teach her to play folk songs by rote. Each "lesson" is usually about five minutes, sometimes less. Little by little, she has learned to play some things. It's not true that young ones can't learn or aren't ready. You just have to move at a slower pace and do things a little differently.
Your son seems interested, and I think he would respond well to teaching. You could start by doing copycat games. Tell him that it's Mommy's turn and he has to listen. Then, it is his turn and he has to copy what you played. Start with rhythms on the black keys, then progress to teaching a song, note by note.
Personally, I would only do the teaching if he is receptive to it. As was mentioned, by exploring on his own, he is already learning. And that may be all he wants to do right now. But some 3-year-olds want to be taught, and you might as well try teaching him. You never know.