[pinnahertz]

So I could use a DI box (active or passive?) And take XLR-RCA cables to feed my headphone amp?

Typically overkill, but yes.  How you would wire the XLR>RCA differs depending on the specific DI box.  
 
Why would you even consider an active DI?  The key here is something called "common-mode rejection ratio".  A transformer has that, even the cheap ones, and to a fairly high degree.  An active box has to fight some pretty tight component tolerances and selection to achieve CMRR even close to a transformer, so the good ones are expensive.  Then you have to be concerned with the cable wiring. Some boxes require cutting the wire to XLR pin 3, others don't. 
 
Here: this is what I use, I thought it was discontinued, but it's still available.  I've tested it, its frequency response is flat down to 20Hz.  Used them for years, and keep several handy. 

 

[mbphotox]

Thanks.. no chance to get this in switzerland. Will get a quality passive DI box from Behringer then.

I don't mind spending 60-100 bucks for this as I listen to music nonstop while working.

 

[pinnahertz]

For a passive DI, XLR-f to RCA wiring should be: XLR pin 2 > RCA center, XLR pin 3 and pin 1 tied together and to shield and RCA outer.

 

[mbphotox]

The support guy at Thomann recommended to buy an ART DTI http://artproaudio.com/isolators/product/dti/

It's a transformer/isolator box that takes all sorts of connectors and kills the ground loop.

And it works!
Even at maximum possible gain, there's not a single blip to be heard, even with my ear directly at the tweeter.
Also, with te tube amp and the headphones, there is absolutely no noise audible.

I'm amazed!