Recently we've seen lots of this small fly in our house in Michigan. They are smaller than regular houseflies and don't have the distinctive green/blue sheen that houseflies have. I assume they bite, because at least once I've killed one and it spewed red (which I assume was blood), although I haven't actually been bitten by one to my knowledge.
The fly is about 8mm in length. They tend to sit on walls or ceilings without flying a lot, and they're not difficult to kill, i.e., they don't immediately fly off when approached unlike a regular house fly.
Is it possibly a cluster fly?
Here are two images. The first image is a live fly, the second is dead which is why the wings aren't flat to the body.
