I just want to add something here that expands on Esfa's last post: Just because a fish is out of the mouth size, doesn't mean that the bichir will not try and take a bite out of them. They are pretty blind animals and rely on their sense of smell more than anything. If there is another fish that has food in it's mouth or near it (like a catfish with a piece of food near it's tail), the bichir may take a bite and take a nasty chunk out of the fish with the food. I've had this happen to me more than once. It doesn't cause any lasting damage on the fish who got bitten, but it's not a nice thing to see.
With the angel fish, I would be worried that the bichirs might think that the ventral fins are a nice tasty worm... I don't want to think about how many times my bichirs have accidentally munched on a catfish whisker.
Just take care when housing these awesome fish. Don't ever forget that they are truly predators at heart and tank mates should be chosen wisely.