In a small bowl, beat cream cheese until smooth. Add hummus; beat until combined. Cut each slice of bread in half widthwise. Spread hummus mixture over 10 white bread halves and 10 wheat bread halves. Top each with cucumber, spinach, red pepper and red onion.
Top white bread halves with remaining white bread; top wheat bread halves with remaining wheat bread. Thread toothpicks through olives; insert into 16 sandwiches.
Arrange sandwiches on a platter or covered board to resemble a checkerboard, placing the green olive-topped sandwiches on one side, black olive-topped sandwiches on the other side and the four plain sandwiches in the center.