Our SharePoint 2013 on-premisis installation is going to be upgraded to SharePoint 2016 in a few months. My understanding is that with the native upgrade option only the databases will be migrated. We have a variety of customizations using Content Editor Web Parts and workflows that would be nice to include in the migration if possible. Is there a third party tool out there that would include these types of features?
Yes, databases will be migrated and upgraded, but inside will be upgraded everything, if you have workflows, pages, etc. Everything will be migrated.
I recommend to do a test migration, when you test migration process and after this verify that migrated and upgraded content is ok and everything works fine.
You dont need any 3rd part tool.