As far as I know (although I only took A-Level and am not up to date with current research...) no one really knows what causes postpartum depression. It's totally possible that the stress of having a new baby around - let alone two! - can make other family members feel depressed. After all, sympathetic pregnancies happen, so why not poatpartum depression too? And you're probably losing equal amounts of sleep, etc.
I hope that was at least a little bit helpful, and that you can start feeling better sooner rather than later (:
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