Cut a thin slice from the bottom of watermelon with a sharp knife so it sits flat. Mark horizontal cutting line 2 in. above center and around the melon.
For handle, score a 1-1/2-in.-wide strip across the top of melon, connecting both sides to the horizontal line. With a long sharp knife, cut all the way through the rind above the cutting line in a zigzag pattern.
Carefully lift off the side pieces. Remove fruit from both sections and cut into balls. Refrigerate the basket.
In a large bowl, combine watermelon and honeydew balls. In another bowl, whisk cranberry juice, corn syrup and lime juice until blended; pour over melon balls. Cover and chill for 3 hours.
Drain; spoon melon into watermelon basket. In a small bowl, beat the cream cheese and milk until smooth. Beat in sugar, lemon juice and cardamom; serve with melon.