Heat a large skillet over medium heat; cook and stir bacon and ham until bacon is crisp, about 10 minutes. Drain bacon and ham on a paper towel-lined plate.
Bring mixed vegetables, potato, water, and onion to a boil in a large pot; reduce heat to medium and simmer until potatoes begin to soften, 12 to 15 minutes. Stir in cream-style corn, whole kernel corn, cream of mushroom soup, milk, half-and-half, bacon, and ham. Continue to simmer until potatoes are completely tender, about 5 minutes more.
