Twice now intense bleed during or after sex...?

Two weeks ago in the middle of having sex my partner informed me that there was blood in some disturbing areas. It was very obvious to me that it was just blood, and not a period, coupled with the fact my period was due in three weeks I highly doubted what that was. We had also had a pregnancy scare just a few weeks before and I still hadn't taken a test, so we thought perhaps it had been a miscarriage early on and thanked our lucky stars we hadn't had time to become attached. When I went to the bathroom later there was also bits of skin or tissue mixed in with the blood, further supporting our theory.

Had sex one time after that, completely normal and nothing happened.

Today I had sex again, and later went to the bathroom only to discover more bleeding, heavier than last time, and also with bits of skin/tissue mixed in. Now my period is due in a couple days so it could be that, except this is straight blood, not period blood.

What is this? How can I prevent it? There is no pain during sex, and lubricant is not a problem (we've tried with and without and it's just really not needed). And ideas?