Place the barley and rice in a medium bowl, and cover with water to 2 inches above barley mixture. Cover and soak overnight. Drain.
Place barley mixture, 4 cups water, and salt in a large saucepan; bring to a boil. Cover, reduce heat, and simmer 25 minutes. Remove from heat, and drain in a colander over a bowl, reserving 2 1/4 cups cooking liquid.
Place 1 1/2 cups barley mixture and 1/4 cup reserved liquid in a food processor; process 2 minutes. Return pureed mixture to saucepan; add remaining barley mixture, remaining 2 cups reserved liquid, sugar, and next 5 ingredients (sugar through figs), stirring to combine. Bring to a boil. Reduce heat; simmer 30 minutes. Remove from heat; stir in rose water, and sprinkle with nuts and pomegranate seeds.