Cut bread into 10 (1/2-inch) slices; remove 2 small end slices.
Spread spinach dip over 1 side of remaining 8 bread slices. Layer 4 bread slices with 1 lettuce leaf, 1/4 ham and 2 cheese halves. Top with remaining bread slices, dip-side down.
Cut each sandwich into thirds, secure with toothpick.