Caps can pass DC
Caps can pass DC.
But when you try to measure it, the cap charges a little, and given enough time, the cap fully charges, and then and only then can you say the cap does not any longer pass the DC. It actually still passes it, it's just that the cap now has a voltage that exactly cancels out the applied DC, resulting in a sum of zero volts at the cap output.
Just use a 10uF cap on the output of a signal generator (with DC offset knob). Then with a 10Meg Ohm scope probe on the other side of the cap (set scope to DC coupling), you can change the offset, and what do you know, you see a DC offset sine. Discharge the cap before wiring, else you'll get an additional voltage offset.
The scope 10 Meg ohms will slowly charge the cap to match the DC offset.
If you use a FET / active probe, you should not see any drift.