In the NFL, has there’s ever been a year where the winners of the Most Valuable Player award and Defensive Player of the Year award were on the same team?
Yes. This is trivially the case in 1986 when Lawrence Taylor won both the MVP and DPoY.
Steve Young and Deion Sanders of the San Francisco 49ers did this in 1994. Young was the league MVP, and Sanders was the DPOY. Aside from the league MVP being the same player as the DPOY (Lawrence Taylor in 1986, Alan Page in 1971), this seems to be the only instance.
In 2003, Jamal Lewis won Offensive Player of the Year while his Baltimore Ravens teammate Ray Lewis won Defensive Player of the Year. Though Jamal Lewis was not the league MVP (split between Peyton Manning and Steve McNair), I find this to be an interesting case worth mentioning.