There are really no good healers and melee'ers combined. Only Priests have regular and powerful healing available. If you are not a priest class, you MAY have an infrequent heal ability. Paladins do have a good heal, but they are a fighter class and will have low DPS.
The best DPS melee classes would be Assassin, Brigand, or Swashbuckler of the Scout class. I really enjoy my Brigand, with multiple attacks, debuffs, stuns, rear attacks, and agro-control. In fact, the agro control is the most fun. If I see the tank getting in trouble, I can jump several places in the hate list to make the mob face me. Then when I need to, I can slide back down the hate list so the mob turns his back. Not wise to turn your back to a Brigand. :)
Assassins have the single highest melee hit.
Here is a link to the SOE page that describes classes.