Good news everyone! ^o^
Tsukina_7mochi has created a lua script for exporting multi-layered Aseprite files to .psd files!! 
You can download it from here: https://github.com/Tsukina-7mochi/aseprite-scripts/tree/master/psd If you have problems opening the exported PSD, you can try using this revision of the script file (right click on the link and choose “save link as”).
If you don’t know how to install scripts into Aseprite you can find how to do it right here.
It is still not possible (to my knowledge at least) to import a .psd file into Aseprite, but at least we have now the export option 