Do transoceanic airliners monitor marine VHF emergency frequencies?
156.8 MHz

Crews don't listen to channel 16 of the marine band.

Channel 16 is used by marine with FM, while a VHF aviation receiver demodulates only AM, and the upper limit of the VHF band for aviation is 137 MHz.

Channel 16 is monitored by local marine agencies -- coast guards -- e.g. CROSS in France and USCG in the US.

Aircraft are only required to carry an equipment able to receive and transmit on emergency frequencies used by aviation.

Emergency frequencies other than channel 16 are also used in marine, including 121.5 MHz, e.g. by EPIRBs. The use of 121.5 MHz for marine EPIRBs was to allow monitoring by aircraft.

Air regulation for listening 121.5 MHz

EPIRBs monitoring by aircraft is not relevant any more as EPIRBs are now efficiently monitored by satellite (COSPAS-SARSAT). However 121.5 MHz is still monitored ("guarded") by aircraft, in particular for interception response purposes. The requirement is specified in ICAO Annex 10 (volume II) to the Chicago Convention:


  5.2.2.1.1.1 Aircraft on long over-water flights, or on flights over designated areas over which the carriage of an emergency locator
  transmitter (ELT) is required, shall
  
  
  continuously guard the VHF emergency frequency 121.5 MHz , except for those periods when aircraft are carrying out communications on
  other VHF channels or when airborne equipment limitations or cockpit
  duties do not permit simultaneous guarding of two channels.
  
  
  5.2.2.1.1.2 Aircraft shall continuously guard the VHF emergency frequency 121.5 MHz in areas or over routes where the possibility of
  interception of aircraft or other hazardous situations exist, and a
  requirement has been established by the appropriate authority.
  
  5.2.2.1.3 Aeronautical stations shall maintain a continuous listening watch on VHF emergency channel 121.5 MHz during the hours of
  service of the units at which it is installed.


ICAO standard and recommended practices ("SARPs") for international aviation activity are recommendations, but they are generally implemented in the national regulations by the member states.

406 MHz

121.5 MHz is being replaced by 406 MHz, as this is the frequency of the COSPAS-SARSAT organization. This organization provides a permanent monitoring worldwide through the use of polar orbit satellites augmented by geostationary satellite relays.