Let's take a close look at fretting the chord.
There's three things to look for.
Your finger touching the lower string, your finger touching the higher string and thumb placement.
Finger touching the lower stringNormally when your finger gets in the way of a higher string (higher in pitch), it's because it's not perpendicular enough to the fretboard. Look at your middle finger, is it possible that is as an angle which makes it touch the B string? Look at the video again and you'll see Christopher's middle fingers as almost an 90degree angle on the fretboard. That makes it possible to play a single string without touching the others.
Finger touching the higher stringThis comes from your finger being too close to the D string. As the D string vibrate, it touches your middle finger and probably does a buzzing sound or mutes the D string. It that what is happening? If so, you need to put your finger tip a little lower towards the B string. As you work on the previous section (trying to be more perpendicular) you'll be able to place your finger lower so it doesn't touch the D string.
Thumb placementThis one isn't always easy to teach. From my experience, not everybody feels comfortable in the same positioning. That said, you can try placing your thumb at the same place as your middle finger. Just as if you were trying to make a clamp using the middle finger and the thumb. Start there and then adjust higher or lower to find the best position that permits you to have a perpendicular finger position on the fretboard and still feels comfortable.
Let us know if this helps you out