Mental illness is stigmatized, you're right about that... but perhaps the best course of action here IS to tell your neighbours that it's not contagious and that they're seeking to get better?

Being "depressed" is no longer taboo... I know plenty of people on antidepressants for 'depression' who I don't think really need them... but it's one of those 'illnesses' that people have begun to accept.

Perhaps sitting down and talking with the neighbours is a good idea. Invite them over - or have a BBQ or something.

Otherwise, simply apologizing for your kids behaviour is a good start. Maybe they feel that they're not sure of how to react, so they'd rather just avoid the problem instead. Except the problem happens to be impressionable kids whose feelings wind up being hurt!

Have you thought about joining a support group of some sort?? I'm sure your area should have support groups for parents, or for those with mental illnesses. Perhaps also finding something that your kids like to do that's constructive (ie. not punching walls or fits of angry expression) would help them to get along better with their peers?

Are they in any sort of counselling or therapy? Have you talked to their teachers at all about their diagnoses? You said that they're getting treatment... does that mean drugs?