[s5e5] Cradle To Grave -

S5E5 - “Cradle to Grave” - Unsubs: A Criminal Minds Podcast

The team initially suspects a black-market adoption ring. However, the profile shifts when they realize the killers are a married couple, Robert and Linda Reinman, who lost their own baby, Michael, due to a medical tragedy. [S5E5] Cradle to Grave

Subplot-wise, this episode features Chief Hotchner being unusually hard on Derek Morgan, a move later revealed to be a test to see if Morgan is ready to lead the team. S5E5 - “Cradle to Grave” - Unsubs: A

The "interesting story" you're referring to is likely the episode " Cradle to Grave " (Season 5, Episode 5), which is widely considered one of the series' most disturbing and memorable "unsub" (unknown subject) cases. Robert and Linda Reinman