If it's common mode, it will appear even on literally the same ground.
The ground of the circuit is quiet. But that doesn't explain why capacitors won't decouple it to ground.
That was first things first. Now we can deal with normal (differential mode) filtering.
Capacitor lead length matters, because physical length equates to inductance. They are proportional quantities. If, shared in common between the PS output loop and the measurement loop, the capacitor lead length is, say, 5mm, then those 5mm ~= 5nH shows up in series with the capacitor.
The length from PSU output to capacitor lead also has inductance. Together, these act as an inductor divider, at very high frequencies. If they are of similar lengths, you won't have much attenuation -- regardless of the capacitor value!
That may be what you are observing here.
Simple fix? Swamp the cap ESL by throwing more inductance in series between the cap and PSU. 1uH would be enough (as you note, 100uH is kind of a lot).
You want sqrt(L/C) on par, or lesser than, the load resistance of the circuit. So, 15V 100mA is 150 ohms, so you might want 50 ohms or less. An R+C2 in parallel with the C helps dampen it further, usually using C2 = 3*C or so, and R = sqrt(L/C).
And yes, the same filter applies on the input side, give or take L and C values because of different V and I values.
The noise measured between grounds may be a problem yet. For this, you need a small capacitor between grounds, and much more inductance. This is because of two things: one, this is a high impedance path, so C should be small, and L large; two, you usually want minimal C here, which means even higher Z and L. The inductance is provided by common mode choke(s). CMCs also have some diff mode inductance (leakage inductance), which can be used with, or as, part of the diff mode filter. This is how typical line filters work, and the same designs and concepts probably apply here.
Tim
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