It doesn't seem to matter how long and how frequent you rest your guys, they never passively heal although the tool-tip suggests they are "recovering" In actual fact you have a better chance sending your wounded and sick out to scavenge and this can miraculously make them better.
I've actually had people that were sick and wounded, sent them on a perilous mission, they got shot and came home feeling great, whereas the people resting on a calm night get worse.
Go figure.