Yes - before any of the coordinating conjunctions for independent clauses.
Clauses are independent when the 'and' clause -(or clause with any coordinating conjunction) - has a subject and verb.
"Basically my wife was immature. I'd be at home in my bath, and she'd come in and sink my boats."
Johnny started to learn the drums when he was just a kid, really practiced hard, and today he is one of the world's noisiest neightbours.
So - in your sentence: "I am happy, and he is happy."