There’s a few ways to tackle it, but all unfortunately involve having two copies of the thread or two copies of the bead. This is because objects and layers have a stacking order, and you’re after an object that’s simultaneously above and below.
You could potentially use clipping masks, compound paths, pathfinder or shape builder, depending if you want to be able to easily make changes later.
If what you’re after is really similar to the image you’ve posted, I’d construct it like this:
- 3 objects, with two copies of the thread. Stacking order of thread, bead, thread.
- The bottom thread object is cut at the bead hole edge, but has a point added that’s been dragged to extend under the top thread. This means the antialiasing will look correct and you won’t ever see white showing through on the edge.
I had a similar problem for an icon I was designing in Photoshop, and tried to solve it as many ways as possible. In the end, all the solutions has duplicated objects.