I'll use an analogy:
If you have a nail and then wrap a current-carrying wire around the nail (some would call that a "coil"), what happens? The nail becomes a magnet. For the sake of argument, we'll say that magnetism is one "thing", and the nail is one "thing". Before the nail has the coil around it, it is a nail. After the nail has the coil around it, it is still a nail. Before the coil was over the nail, the magnetism was magnetism. After the coil was around the nail, the magnetism was magnetism. Neither the nail nor the magnetism changed. But once you put the coil over the nail, the entire nail became magnetic. If you were to be able to put a piece of metal to the nail at any point on the nail, the piece of metal would stick to the nail. On all points of the nail, it is both fully nail and fully magnetism. They are not combined into one whole new substance, yet it is impossible to separate the two. You couldn't get a microscope and differentiate between magnetism particles and nail particles. It is one magnetic nail.
It is similar with Christ. The Word became man. Man is not a soul trapped in a body. Man is soul AND body (some would say body, soul and spirit, but that's a different debate). God didn't become a human soul. God became man. God became ALL that man is. In fact, John uses the verbiage, "and the Word became flesh". He didn't just take on a soul; He took on flesh. The Word became united to all that we, as "man", are. The entire person of Jesus Christ was entirely God-man. It's not that God "fills" the body of Jesus from the inside. Rather, Divinity and humanity are fully united in One Person.
Make any sense?