Are you using the "Scale Automatically" option when you import the .bvh?

The simplest way to correct this problem is to use the BODY's yTran dial to offset the figure's position. However, if the mocap isn't particularly clean, the figure's altitude might vary throughout the animation, and you'll have to keyframe new yTran values at various points to ensure that it remains at ground level. The downside of using BODY is that it won't automatically be saved in pose files or .bvh files.

You can also adjust the hip's yTran values, but as these are already keyframed throughout the animation, the best approach is via the animation graph (as shown above). You can select a range of keyframes, and then shift them vertically by holding down the CTRL key.

If you have Pro Pack, P5, or P6, you also have the option of using a Python script (dropFigToFloorAllFrames), which will adjust the hip's yTran keyframes automatically.