Combine the black beans, black-eyed peas, corn, celery, cilantro, red bell pepper, tomato, onion, pimento peppers, jalapeno pepper, and garlic in a large bowl.
Pour lime juice and Italian dressing over bean mixture and stir until dressing is evenly distributed. Cover and refrigerate for at least 2 hours or overnight.
Serve with nut thins, tortilla chips, and/or carrot chips.