Animations Affect My Game Object's Z Position

Hey guys. I am having a bit of trouble with my animations. They work great, but I have a character set up with a plane as the ground. The more I go through the animations, the character actually begins to slowly fall through the plane. Eventually he falls straight through. I tried Baking the X and Z axes to the animation, thinking that might do something, but it doesn't. Rigidbodies and Colliders don't matter. The character falls through with or without them and I don't think adding either of those physics things speeds up the process. Not sure what's going on. Any help is appreciated. Thanks guys!

EDIT: I actually tested with a rigidbody again. It seems that with JUST a rigidbody (no colliders), the higher the number, the faster the character sinks, and vice versa. A mass of 1 makes my character float in the air.