Bec - my experience with the assessment process is that if you demonstrate you have sought help for the issues, this won't work against you. I had some fairly large trauma in my life over 10 years ago and this came up alot through my assessment process. But I was able to demonstrate I have worked through these issues, sought out supports and there is no daily affect on my life.
When you begin assessments the social workers would have identfied the mild depression in your DH, so it is probably better it is in the report from the doctor as it shows your DH has been seeking help.