Can I play minecraft with my friends on Xbox 360 if I have an Xbox one?

Sadly no. This is Xbox's way of making you pay money to buy their new console. It sucks I know. The reason this is the case is because the graphics and code for the Xbox 360 and Xbox 1 games are different. So therefore the Xbox 360 cannot compile Xbox 1 code. Which in turn means you cannot play multiplayer games with one person on an Xbox 1 and one person on an Xbox 360. So unfortunately you or your friend would have to buy the other console.

Unless they don't make the Xbox 360 version availible for Xbox One, you won't be able to play on it because both systems have their own network servers. Xbox 360 games which are compatible with Xbox One will work.