Play online with an Xbox One person using Xbox 360.

You can also play World of tanks between the Xbox 360 & Xbox One. More info here https://worldoftanks.com/en/news/announcements/world-of-tanks-xbox-one/

If you want to play a backwards compatible game with them that will work! Here's a list of the backward compatible games: https://www.xbox.com/en-US/xbox-one/backward-compatibility/available-games

When playing on the 360 each person would need to have a Gold membership if they wanted to play online.

If you were using an Xbox One only one person would need a Gold membership to play. That membership could be shared amongst all family members on the Xbox One console.

If you are playing on an Xbox One console then one person can share the Gold membership. However, each player would need to have a membership in order to play online on the 360.

Its more than possible, its real. If you've got a game that has multiplayer or co-op and you're playing it online on the Xbox 360 you're bound to have run into an Xbox One player at some point. Assuming the game is something with backwards compatibility
features. The Xbox One runs what's basically a simulation of the 360's UI to play backwards compatible games. However, its impossible to play two different versions of a game. You can't play a title that was released on the 360 and the Xbox One and expect
to be able to play it with the person who has the Xbox One version. So basically you can play 360 games online or offline on the Xbox One but not the other way around.

Here's about backwards compatibility. https://www.xbox.com/en-US/xbox-one/backward-compatibility

In short, can you? Yes. Just only on Xbox 360 games that are compatible with the Xbox One.