As you've clarified that you only use the unbleached flour mixed with wholewheat, then yes, you can store the blend, and it will keep just as well as the individual flours. So if you get through large quantities always in the same proportions, go for it; if the proportions aren't fixed it seems more trouble than it's worth.
Let's assume you normally make a recipe that uses equal weights of both (50% wholemeal recipes are common in breadmakers for example). A well-mixed 50:50 blend would allow you to just use the same total weight, which is easy. But if you want to make a 70% wholemeal one day (you do, after all, sound like you want to keep up the wholegrain fraction of your diet) you have to fiddle about with the maths. You can also use just the wholemeal for flouring the worksurface or dusting a loaf. It gives the crust a nice flavour and texture, especially if you use stoneground or a similar slightly rough flour. The blend wouldn't have as much of this effect.
If you always make the same recipe, why not add the other dry ingredients (in the correct proportions of course): the baking powder for cakes or quickbreads, the salt and sugar for yeast breads (but probably not the yeast). You could even pack it into containers holding the right quantity as a batch process, essentially assembling your own mixes.