I think this really depends on the individual. My in-laws, for example, really don't understand what it is that I "do", yet they know I work from home. I am not accountable to them, so I do not go into great depths trying to explain it, but they are not the questionning type.
My husband, on the other hand, has always been supportive of my business. However, until you are actually earning an income, it can be challenging for a spouse to keep believing if they are not directly involved with what you are doing, especially over an extended period of time.
I know how challenging it is to keep on believing for me, and I'm in the midst of it all. Now that my business is starting to see "fruit", my husband is starting to come up with his own ideas, too!
My husband, my sons and my daughter are the only people who I am really concerned with regarding the opinions of my business.
Hope that helps!
Patty