The other 2 answers given for this question, are wrong. The situation described will be given as six i.e. six runs will be awarded to batting team.
I know these answers were given 7 years ago, so maybe the rules were different then.
But AS THE RULES STAND currently , this will be a six.
The relevant law is as follows
19.5.2 A fielder who is not in contact with the ground is considered to be grounded beyond the boundary if his/her final contact with the ground, before his/her first contact with the ball after it has been delivered by the bowler, was not entirely within the boundary.
So, since the question says "Then he jumps from outside the boundary rope and fields/catches the ball and sends it back to the other fielder while in the air" , so this clearly means that his final contact with the ground before his first contact with the ball, was outside the boundary.
So, according to the rules, when he first touched the ball, he was grounded outside the boundary (even though he was in the air at that moment) . Hence, this will be judged as a six.