Dana, as a hospice volunteer, I heartily recommend you reach out to them. Most towns have volunteers who will provide help. They can send volunteers for peer support for your parents.
Your parents might benefit from Meals on Wheels, or other supports like that. There are many senior agencies where you might purchase services.
Give your father permission to be sick.
It is not surprising that this might happen, depression, on the other hand, when we are ill we tend to go inwards. Protection from society, others.
The Cancer Society with give you peer counselling. I had that when my mom was dying of cancer having chemo, dad's brain tumour returned, and he was getting radiation.
I ended up on antidepressants myself, and burned out working while trying to be caregiver.
Look after yourself.
I called the cancer society for help. They provided me with much information, from research, on things I could do. They also hooked me up with a woman, by phone, whose mom had died from a brain trumour, and father had had cancer.
You are not alone.