While the medical industry pressures people to get treatment, that takes time and money at a point when families have less of both. Due to the nature of the triggers -- hormone swings and a crying baby -- this type of depression is often temporary. Notice how they say it takes months to clear up on its own, but also months to clear up with treatment. How much is that treatment shortening the duration? Possibly not much if at all. Sometimes people just want to feel like they're "doing something." I'd like to see a comparison between talk therapy, pills, a free nanny, and say $500-1000 a month extra to pay for baby expenses. I suspect the latter would be more effective than the former, except in cases where the prevailing cause is biochemical imbalance (more likely in mothers than fathers).
In more practical terms, you can help reduce the chance or impact of this problem by offering to do housework, go shopping, or watch the baby/older kids so the parents can get some freaking sleep. Postpartum depression can hit anyone, but it's much more likely to affect parents who are overburdened and underslept.