Hmm... I personally doubt that it is due to your depression, but to be quite honest we could guess all night and never even come remotely close as to what the problem is. If you wish to solve it then you need to find out exactly what it is.
What your boyfriend should do is wait until there comes a time when his father seems colder and more uncomfortable than normal - and then just simply ask something like "What have you got against her?" or "What was that for" etc. I personally can see that this is the only way you could really get an answer............. other than this other way...
Another way, relies on his mum and dad having a good relationship and that he has a good relationship with his mum. Couples usually talk to each other about matters such as their childs partners, and therefore if there was something wrong with the dad then the mother would most likely know.
Sorry that's all I can give at this hour