MSSQL Server - Mirror Between Different Versions
Technically it can work, although it's not usually a good idea to do so as part of a DR strategy, as after you've failed over to the newest version, you can't easily fall-back to the older version. The only reason it is supported is for doing rolling upgrades and minimising downtime. 

This MSDN article explains all about it. 

Some additional thoughts not strictly in answer to your question, but that come to mind:


I can't think of a good reason for keeping a system on an old version of SQL Server when you have access to a newer version. You're not going to be able to use any of the new features of the newer version, and you could run into development problems (particularly if you ever failed over to the newer version, made changes only available in 2016 and then wanted to go back to the older version - which would be tricky to do with mirroring like that anyway, but impossible if you've used something not available in 2008, and it could cause you to end up in hot water). I suggest just upgrading your main system to the most recent version you have access to.
Bear in mind that SQL Server 2008 is coming to it's end of life, and is in the process of being put out to pasture/sent to the glue factory. 
Mainstream support ended two years ago, and it'll be totally out of support in 2019 (and they're not releasing any more updates anyway).