Drain and rinse the corn, black beans, and black-eyed peas, then add them all to one big bowl.
Dice the red bell pepper, Roma tomatoes, and jalapeño and toss them in. Leave the jalapeño seeds out for a milder bite.
Chop the cilantro and add it in.
Fold in the diced avocado so it stays in pretty chunks instead of turning to mush.
Sprinkle the zesty Italian dressing mix over the top and squeeze the limes over everything.
Gently mix it all together and add salt and pepper to taste.
Cover and chill for at least 30 minutes so the flavors can meld, then serve with tortilla chips.