Frequency has nothing to do with it, or more particularly -- you don't want to think about frequencies where it does, because then you need to work with all the fields.
Confining the question to low frequencies, only electric field is needed, and the problem is electrostatic. Literally, electric, not moving.
If you have four layers: metal, dielectric 1, dielectric 2, metal, then the total electric potential is the voltage between plates. The average electric field is the potential over the distance between plates (assuming infinitely wide plates). The electric field divides between the two dielectrics according to their thickness and constant.
A higher dielectric constant is more "conductive" (permittive) to electric field, thus drops less electric field than a higher K material, when those materials are connected in series.
You can draw an equivalent circuit as a resistor divider, where resistance is actually capacitance, and current is actually charge. The usual capacitors-in-series formula then applies.
Which seems to be your intuition, and I'm not sure where you're coming from with the premise that it would be the other way around?
Tim