Place all berries in a blender, and process until smooth. Press berry mixture through a sieve over a medium bowl using the back of a spoon, reserving 1 cup puree; discard seeds. Reserve any of remaining puree for another use; store in the refrigerator.
Combine sugar, cornstarch, and salt in a medium, heavy saucepan, stirring with a whisk. Stir in 1 cup puree, juice, and eggs. Bring to a boil over medium heat, stirring constantly with a whisk. Reduce heat, and simmer 1 minute or until thick, stirring constantly. Remove from heat; add butter, stirring gently until butter melts. Cool.
Spoon mixture into a medium bowl; cover and chill for at least 6 hours or overnight (mixture will thicken as it cools).