Driven mic'd guitar amps monitored through the UR242 headphone Jack sounds buzzy

My mic’d Fender Reverb Deluxe amp sounds great through the Steinberg UR242 headphone jack as long as the guitar sound is clean. As soon as I add a little overdrive to the amp, the sound in the UR242 headphone jack gets all buzzy. Setup includes:

Amp: Fender Reverb Deluxe
Stereo Recording Isolation Cabinet
Mic 1: Shure SM57
Mic 2: Sennheiser e906
16-ohm headphones, closed back
30-ohm Philips Audio Fidelio X2HR open back headphones
250 -ohm Beyer DT770 Pro headphones, closed back

Any way to correct this?

How is the gain structure?
Do you listen direct or via daw?
How is the dspmixfx set up?
How does the guitar sound recorded?