'Untenable' is used suitably for the sentence you have said as an example.
The sentence : "The situation in their marriage became untenable" says that their relationship for certain will fall apart; there is no way so that they can still live together as a wife and husband.
in return adjective ' unbearable' we can use e.g,: an unbearable pain (= the pain makes you upset and annoyed)
Correct me if my way of apprehension is wrong;)