In addition to spliting the birch small, try and peel some of the bark away. When birch is split, often there is a reasonable amount of bark to grab onto. This will help to accelerate drying.
Quick bark inspection for insects, then save bark in boxes for kindling.
New white birch limbs can start off a black-brown color. The same can happen on gray birch, which is lower on the BTU food chain. Gray birch bark often looks like what I would envision as white birch that was sick. That said, free is free. ALL of the wood I burn is was not paid for. . . only secondary, smaller costs, like gas and time to load it into my vehicle and drive it, buck, split, etc.
The "dark stuff" could also be yellow birch or black birch, both I believe are higher BTU than white . . . although not in the realm of sugar maple or the oaks. Probably all from the same tree, though, and thus, white birch.
Good luck.