Design steps for a choke inductor
You have drawn a differential choke not a common-mode choke - a CM choke has dots at the same end and doesn't easily saturate because current flowing sets up cancelling flux thus nearly entirely preventing saturation. The differential choke in your circuit very easily saturates because the fluxes from the two coils are additive.

The CM choke blocks only common mode currents i.e. currents of the same direction trying to enter and pass through the choke - this is a good example of transformer action. For differential currents (as per the signal you want to pass) the windings are in effect anti-phase and have a low impedance: -

impedance = \$j\omega (L - M)\$ where L is the inductance of a winding and M is the mutual inductance between windings. M is usually very close in value to L therefore the net inductance for differential signals is lower than for common mode signals. For common-mode currents, the impedance is \$j\omega (L + M)\$ i.e. significantly more than for differential currents.

I get the feeling that you are expecting a CM choke to deal with high frequency differential currents differently to low frequency currents. This is theoretically not the case but, in reality, because leakage inductances exist (not all the flux is shared between the two coils), there is a tendency for higher frequencies to receive more attenuation.

For more info read this on page 6