Storing Whole Wheat and Unbleached Flour
Whole wheat flour has a lot of fat in it and will go rancid relatively quickly. It should be used promptly after it is ground or frozen for long term storage. Even if it will be used soon, keeping it cool and sealed from air and light is helpful.

There is no adverse effect from mixing flour types. Keep in mind that separately your white flour would keep much longer but your mix will only last as long as the wheat flour.