In a small saucepan combine sugar and 1/2 cup water; bring to a boil over medium-high heat, stirring until sugar dissolves. Lower heat and simmer 3 minutes. Cool completely. Stir in lime juice and mint. Cover syrup and refrigerate until chilled, at least 1 hour.
In a large bowl combine honeydew and cantaloupe cubes. Add syrup and jalapeno and toss to combine. Serve melon with a little syrup spooned over.