One thing you can do is make the material invisible only after it goes through two layers of transparency, rather than just one, by adding a greater than node:
The transparent depth output is incremented each time the ray goes through a transparent surface.
With your current setup, it is used to mix between a partially transparent shader and a completely transparent shader based on the number of transparent surfaces the ray has passed through. The partially transparent shader is used if no transparent faces have been encountered, and the completely transparent shader is used if more than 0 transparent surfaces.
For example, the logic looks something like this:
if transparent_depth >= 1:
Since you put another transparent surface in front of the sphere, you need to allow for that by only making the shader completely transparent after at least two transparent surfaces have been encountered.
By using a greater than node like in the setup above, the logic should look more like this:
if transparent_depth >= 2: