There are several reasons that they keep coming back.
I see that you mention that you have only treated your heads.
Lice are similar to fleas in certain ways. They lay eggs, and also live in carpet (for short amounts of time), can hitch rides on animals (for shorts periods of time) as well.
Carpets need to be vacuumed thoroughly once a day for a week.
Sheets need to be washed in hot water and dried in a dryer. (Towels too)
Stuffed bears (stuffed animals) - if they can be washed, wash them in hot water. If they cannot be washed, place them in a trash bag for 1 week.
Couch/sofa furniture - vacuum it thoroughly once a day for an entire week
Brushes and combs should be placed in the dish washer (use the silverware rack) to be sure it kills the eggs.
If you have used it, laid on it, thought about laying on it, you need to use a spray, vacuum it or bag it for a solid week to be sure you stop the egg cycle.
Hair wise: Comb thoroughly on day 1, use some method to get rid of knits as well as the live lice. Comb through again thoroughly on day 3, and again on day 6. It is easier to do this in direct sunlight because the knits actually kind of 'gleam' or 'sparkle' in the sunshine. Silvery.
Also, as bad as it sounds, be sure to check leg hair, underarm hair, pubic hair, and any other part of your body (and tell your family to check their bodies too) for lice and nits/eggs.
Yes they will travel 'south'.
My family and I live in the south. Head lice is common. Personal experience of having recurring headlice for three months will make you very aware of how to take care of the buggers!