The 'Love Me Now' hitmaker and the 31-year-old model's fans regularly dub the couple ''relationship goals'' but John insists their lives are certainly not ''perfect''.
He told TIME magazine: ''My wife just wrote very candidly about what she went through with postpartum depression and dealing with the aftermath of having a child.
''We're very happy in our relationship and very happy to be parents, but, like everybody, we're human and we have challenges. No one should think that our lives are perfect.''
Meanwhile, Chrissy previously admitted she thinks ''it's kind of silly'' that people look up to her and John's marriage.
Asked how she feels when people constantly say she and John represent ''relationship goals'' on Twitter and Instagram, she said: ''I do think it's kind of silly. I love being that way, because I love people looking up to somebody who has a relationship that's enviable, of course. But also, the things they say it for are so stupid, like, we'll be eating a burrito and someone will be like, 'Relationship goals!' and I'm like, 'Go get a burrito? Just eat a burrito!'
''We should definitely have higher standards of relationship goals, but at the same time we're very happy to be people's relationship goals.''
And the couple - who share 12-month-old Luna together - admit they row about ''normal'' things just like any other couple.
John said: ''Chrissy and I bicker about the normal things like, 'When will you be home from work?' I also look at my phone too much ... Twitter, Instagram, texting. She occasionally tells me off for that.''
Speaking about their daily routine, he added: ''Chrissy and I cook to relax. I've very good at making fried chicken, macaroni cheese, omelettes and pancakes ... Then we just hang out and watch TV. Netflix and chill, as they say.''
Corgan took to Instagram to confirm rumours of new Pumpkins material, saying the first songs could arrive as early as May.