Can a mice infestation make you sick?

we've had difficulty getting rid of mice in our new house this winter. Sure, we keep food in the cupboards and every morning I wipe down my entire kitchen with bleach water from head to toe so we aren't eating on anything the mice might have crawled on, but despite the precautions I'm concerned about the pet food dishes and from time to time we've found the odd evidence they've stolen some food and stashed it (maybe during the day from a box of cookies when we went out on a walk or something) and we find piles of mouse poop in areas of the house we don't expect, like my daughter's toy bin (she still mouths all her toys) or behind our couch on all our NEW baby furniature we're saving for when I have my new baby in a few weeks. Can the presence of mice make us sick or give us an illness? Please, only answers from people who actually HAVE an answer, (no speculation plz, it doesn't help). incidentally I've had the flu for two weeks - could it be a mouse related thing and not a flu at all?