There are ways of getting media and sequences back and forth from Avid but it takes a lot of effort/testing/troubleshooting. Avid prefers to use OP-Atom media (video and audio in separate files), it can use OP1A MXFs but you will have to set it up for that. Where is the media coming from?
You will be able to do it with enough effort but you will probably hit some hurdles. I recommend one of you switches NLE. The learning curve will probably be less painful than trying to send AAFs back and forth.
If the DIT makes Avid Bins as per the spec, then obviously you won't be able to open them.
Premiere will be fine with DNXHD115 OP1A MXFs. But you will have to speak to the DIT to let them know you intend to bring the media into Premiere as well (otherwise they might assume a full Avid workflow and create OP-Atom media with audio syncing done in an Avid bin rather then encapsulated into the OP1A media files).