I'm not sure if DB sells mobile Interrail passes but you can buy an Interrail pass anywhere you like and that doesn't make a difference for the validity. Your country of residence will remain Switzerland.

The Bahn Card have nothing to do with Interrail (means you get no discount or something for Interrail)

Yes you can buy Interrail on the ticket offices (“DB Reisezentrum”) or online at bahn.de but in my experience that would be the paper passes (I still prefer them ) 

@seewulf 

As holder of BahnCard I did get a DB-mailing today telling me I could buy the Interrail Mobile-Pass at 10% discount. 
I will try to phone them tomorrow.

The 10% discount is not for BahnCard holders but for everyone. It is offered by Interrail.

As far as I can see, DB forwards you to the Interrail website with a DB stylesheet.

@rvdborgt 

I am aware of that.

The only thing I am unsure is if I am eligible to this offer or not, giving that I am not living in Germany. Txs!

Sure you're eligible. You don't even need to buy it via DB.

Rvdborgt, is right