Under unbiased condition, commonly MOSFET would symmetric source and  drain . But under  applied biased  there is  no    symmetric between  source and  drain.

Does that means that source and drain must be interchangeable?

Yes, MOSFETs can have asymmetric source and drain. Many researchers are doing such type of researches and have found some good results on especially mobility without affecting any transistor actions.

Asymmetric in the sense on the basis of doping concentration, structure size etc.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4061658&tag=1

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5563530&newsearch=true&queryText=asymmetric%20source%20and%20drain

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=1015441&newsearch=true&queryText=asymmetric%20source%20and%20drain

Hypothetically, drain and source are interchangeable and they are symmetric, however in real situations the source terminal is connected to the body; so that the body-diode will change certain performance when it is forward bias. If you would like to read research on these please check https://www.researchgate.net/publication/274701915_An_extra_low_frequency_RS-SCALDO_technique_A_new_approach_to_design_Voltage_Regulator_Modules also available in IEEE http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=7104629

Conference Paper An extra low frequency RS-SCALDO technique: A new approach t...