Dysthymia is considered as a form of depression, as you say a 'mild' form of depression. It's common that it runs in families but may not be the case.
What I do want to mention is that over 50% of people diagnosed with Dysthymia will develop major depression.... so yes I agree with you that this should not be ignored. Is there anything that you think could be causing your husbands depression? E.g. Money problems, work, stress? Often seeing a 'self-help' therapist helps. These are not qualified counselors, but are trained to talk with and listen to a person and work with them (through writing activities and such) to help them see why they are depressed and recover from it.

Please keep trying to find someone who will help your husband, there will be someone who will agree with you that he needs treatment/help.

Best wishes, Molly