You should be able to create a DC offset to your input signal by using 2 resistors (connect them from GND to +5 and connect them together at the other ends) and connect the center point via a capacitor to your input signal source on the one hand, and connect the center point directly to the input of the analog switch on the other hand. In this way you superimpose the AC of the input signal on the DC in the center point. This is how AC-coupling is frequently done in amplifier stages where you need a DC bias voltage for the next stage but only want the AC of the previous stage.
B.t.w. you can do fun things with analog switches and digital circuitry. Have a look here: PWM fader experiment