You are an oscilloscope! How AC and DC coexist
Grab a piece of paper and draw a sine wave(or imagine that you did). Label the height of the wave peak to peak. So now we have an AC voltage. Now sit down and hold the piece of paper. Sitting down is 0 volts DC. Now stand up while holding that piece of paper. Standing up=100VDC. Your sine wave is still the same AC signal but now it is sitting a little higher on a DC voltage. The AC wave has its own values(the height of the wave does not change according to what DC component is present). The sine wave you drew did not change when you stood up, it just moved somewhere else.
AC can sit on top of any DC Level referenced to ground. AC is just a uniformly changing level(wave) over the passage of time. The offset of that wave from the reference is the DC component. The actual top and bottom of that wave is the AC component. The beginning of one wave to the next is the period of the wave. Frequency therefore becomes 1 divided by the time it takes for that one period.
Let’s take an audio amplifier for instance. Transistors in an amplifier need VCC(DC) to turn on and amplify an AC signal (the audio). Now you need to get rid of the DC before feeding the signal into the base of the next stage, hence a coupling capacitor is used. The DC level simply turns a semiconductor on so it is able to manipulate AC in this case.