I would hazard a guess that this is "Aquarius Mission" by author Martin Caidin (who also wrote "Cyborg", the inspiration for "The Six Million Dollar Man" series).
I can't find a good online summary to let you check the plot summary (it wasn't a great book), but the basics as I remember them are:
* it's post-nuclear-war on the surface (though this does not get much attention in the book)
* a deep-sea submarine is destroyed by attacking sperm whales
* a new, armed deep-sea sub is sent to find out what happened, and they get past the defending creatures to an undersea zone inhabited by "merpeople"
* much political wrangling goes on within the merpeople society about how to deal with the arrival of the surface people
Other minor details:
* a teenage girl who is an unlikely member of the mission marries one of the merteens
* the merpeople have some kind of huge organic computer
* there is an invasion of the merpeople's zone by extremely dangerous acidic jellyfish near the end, in which the surface humans turn the tide using some sort of beam weapon rifles (gamma ray laser?)
