Assuming that by "depth" you mean that a picture book has a serious point, and that by "story layers" you mean that a picture book has interrelated multiple narratives, a few recent books that come to mind include:
Depth:
Grandma's Gift, Eric Velasquez (2010)
Zayde Comes to Live, Sheri Cooper Sinykin (2012)
Sophie's Squash, Pat Zietlow Miller (2013)
Lilly's Purple Plastic Purse, Kevin Henkes (1996) (older, but an excellent portrayal of a child's emotional landscape)
Shi-shi-etko, Nicola I. Campbell (2005) (also older, but remarkable for how the author communicates a very difficult historical context)
Story Layers:
One Cool Friend, Toni Buzzeo (2012)
Lost and Found, Bill Harley (2012)
Mr. Wuffles! David Weisner (2013)
The Long, Long Line, Tomoko Ohmura (2011)
Hope that helps!