Tell him he needs to put his oxygen mask on before he can put it on your DD. If he wants her to be mentally healthy, he has to work to get himself mentally healthy. It is hard when this stuff runs in your family because you either got help or you didn't depending on how your family handled the problem, but the real issue with mental health challenges is that there is a serious stigma out there with regard to these things to the point where the person who has issues thinks negatively about themselves and then doesn't feel worthy of getting help.
BUT if he wants to create a healthy childhood for her, he has to work to make that so for himself, medically and/or with cognitive behavioral therapy, whatever is best for him.
In addition, as you have noted, there is a component to some of these things that make everything look "through a glass darkly" basically no matter how good things are, the depression makes things look bad. This is often a chemical thing so please see if he would consider a trial of antidepressants if a doctor suggests it.
Unfortunately telling the dad not to be depressed is like telling a person with diabetes to just eat the right way to keep their sugar down… it may work for someone who has very mild depression but if he really has a problem only medicine will help him.
BTW some or none of what I have written above may apply to your husband- I have made a jump based on the very little information you have included. But I have experience with mental health issues in the family and so I thought I would chime in. Depression can be a very serious problem, and stigma can keep people from getting a handle on it.
