Many times the question has been asked, can I not add my Exchange 2010 Server to my Exchange 2013 DAG or my Exchange 2013 Server to my Exchange 2016 DAG.
Well, the answer is No you cannot. Let me explain why.
Firstly, your Exchange 2010 Servers are probably running on Windows Server 2008 R2 Enterprise and your Exchange 2013 Servers are running on Windows Server 2012 or R2. The clustering is different in the 2 versions and you cannot mix Operating Systems. They have to be on the same level across all the DAG members.
The second problem is, you cannot do an in-place upgrade on an Exchange 2010 Server. This is firstly not supported by Microsoft and Secondly you will break your current Exchange Installation.
The database engine is also different across the different Exchange Versions. For those that are running Exchange 2016 RTM (You should have upgrade by now), there was a bug in this version that allowed you to add an Exchange 2013 Server to an Exchange 2016 DAG. Please take note, this is not supported at all by Microsoft and I strongly advise against trying to do it or take the easy way out.
Here is information from the Release notes for Exchange 2016:
Mailbox servers running different versions of Exchange can be added to the same database availability group The Add-DatabaseAvailabilityGroupServer cmdlet and the Exchange Admin Center incorrectly allow an Exchange 2013 server to be added to an Exchange 2016-based database availability group (DAG), and vice versa. Exchange supports adding only Mailbox servers running the same version (Exchange 2013 versus Exchange 2016, for example) to a DAG. Additionally, the Exchange Admin Center displays both Exchange 2013 and Exchange 2016 servers in the list of servers available to add to a DAG. This could allow an administrator to inadvertently add a server running an incompatible version of Exchange to a DAG (for example, adding an Exchange 2013 server to an Exchange 2016-based DAG). There is currently no workaround for this issue. Administrators must be diligent when adding a Mailbox server to a DAG.
Unfortunately there is no easy way out. If you want to move to Exchange 2016, you will have to build a brand new DAG and migrate your mailboxes across from Exchange 2013. Rather be safe than sorry in the long run.
Hope it helps.