The device substrate has inherent diode between source and substrate and drain and substrate. These are called body diodes in spice models. In a discrete MOSFET the substrate is usually tied to source shorting out the source-substrate diode, so the drain to substrate diode will be the pertainent conduction when reverse voltage is applied. The device substrate diode will give 0.6 to 1.0 vdc voltage drop depending on current. If you also apply gate drive the normal MOSFET channel will conduct, in parallel with substrate diode, and you can get lower voltage drop then diode forward conduction voltage, assuming the channel Rs of MOSFET is low enough.
You can create a bi-directional conduction with two MOSFET's connected drain to drain, or source to source, in series. For AC current, the difficult part is driving the gates which has to be isolated from the bi-polar AC voltage. Typical gate drives is from pulse transformers which provide the necessary isolation.
For I.C. analog switches, like CD4066, there is a P-ch and N-ch tied in parallel. The P-ch body diodes are tied to Vcc positive supply. The N-ch body diodes are tied to Vss negative supply. Analog input must stay within the Vcc to Vss voltage range of the I.C. supply or the body diodes will conduct.