If you want to fill the region, you should use only one path
element. You can chain the bezier curves together so that one starts where the last one ended. Then, add Z
to the end of the path data to close the path.
<svg xmlns="http://www.w3.org/2000/svg" width="500" height="300">
<path d="M480 150 C 300 200, 200 150, 20 200 C 15 150, 15 150, 20 100 C 200 100, 300 150, 480 150 Z" stroke="black" fill="red"></path>
</svg>
If you know where all of your end points and control points should go, it's no more difficult than making separate paths.
Here's a FIDDLE if you want to play around with the path data and see how the chaining works.