INTERSTATE 80, Nev.—Many couples and empty-nesters dream about traveling the world together. Some are making it a reality—in the cabs of 18-wheel freight trucks.

On a recent Monday night, Karen and Paul Lucey and their dogs, Sammie and Earl, left home in the Bay Area to pick up a load in Hayward, Calif. Then, as they do almost every week, they started out on a six-day, 6,000-mile trip to New Jersey and back.

Mr....