Is there any device for measuring phase and gain of a device in frequency range as low as 0.1 Hz?
If you can get a hold of (rent or buy used) an HP/Agilent 3562A dynamic signal analyzer, it can handle the job from 64uHz to 100kHz.  You can use a conventional frequency response analyzer for the higher frequency range.

I got one years ago for $400 on eBay, but there are ones in better shape easily available (for more $$): 

3562A

Of course your measurement time for sub 1Hz testing is going to be long if you need a lot of points.