For each sandwich, place 1 ounce each of turkey, ham and Swiss cheese between two slices of whole-wheat bread. Slip sandwiches into egg mixture, turning frequently to soak both sides.
Place a large nonstick skillet coated with cooking spray over medium heat. Put sandwiches in skillet and cook each side until golden brown and cheese is melted, about 3 minutes per side.
To make dipping sauce, combine red currant jelly, Dijon mustard and orange juice in a small skillet over low heat; whisk mixture until blended. Transfer sauce to four small dipping bowls; serve with warm sandwiches.