Yes, you're seeing that correctly...this card has TWO DIFFERENT TYPES OF ATTACK! He does both a Magic and Melee attack each round!
Do the attacks occur at the same spot in the order stack? For example, does the magic attack always come directly before the melee attack? Or can these two attacks be separated with other monsters of the same speed in between? The former is more like double strike. Also I'm guessing the heal triggers before the first attack?