Depth of field and antialiasing with transparent images

Hello everybody, I have a problem with my rendering using eevee.

I am rendering on a transparent background. The problem that I am facing is that the depth of field effect is gone in the rendering.

This is a screenshot of my 3d viewport,

And this is the rendering

The first thing that I have done was to increase the filter size from 1.5 to 12. This is more or less solving the antialiasing problem, but the depth of field still looks gone, or at least really different from what I have in the viewport.

This problem happens only with transparent background, with a color in the background everything works consistently between the render and the viewport.

I have found online this old post, but the blender interface is now different.

Any idea about to solve this?

Do you think that I have to play in the compositing tab to get it working correctly?

I have tried to use the defocusing node in the compositor but without achieving the desired result.
I have read also this thread

But I am not using a transparent material. Do someone have a suggestion?

It looks like a known problem

I am downloading now the alpha release to see if it is fixed there