Capacitor with pulsating dc voltage source/current
Maybe this image helps you understand:



From the time domain point of view you might think of this "pulsating DC" concept and think that it should pass over the capactior.

From the frequency domain point of view, there are two different components, the DC (0Hz) and AC. If you put a capacitor in series, you are using a High Pass Filter, meaning that the DC component will be filtered and won't pass.