Writing this post here as the previous post detailing this issue was not placed in the bug report forums. (Link to other Forum Post)
Effectively, it appears as though queueing into Blitz solo as a healer or DPS can prevent that character from queueing duo Blitz.
Here’s how I produced the issue on 2 characters, both healers (resto druid and resto sham). I also had a friend test it on his DPS (balance druid) and that DPS was unable to queue Blitz with my 3rd fresh healer (pres evoker).
Queued for blitz twice on Rdruid solo. Lost both games. After the second game I attempted to queue with my friend (balance druid) but we were unable to get the group finder to put us in queue.
I then hopped on the rsham and attempted to queue with balance druid. The group finder allowed us to queue up. We left queue and I then had my friend log onto his DH, and test with the shaman again. The group finder once again let us queue. We left the queue once more and solo queued on the Rsham and on the Balance druid.
When I came back from the blitz, we grouped up again (rsham and balance) and we could no longer queue blitz.
I logged back into my resto druid and grouped up with the balance druid to see if maybe now that we’ve both played at least one game that would solve the issue. The issue persisted however. We did not though, that if he chose healer and I chose DPS, we were able to queue together.
I then logged onto a preservation evoker that had not queued blitz yet, and my friend logged back onto his DH. We queued for a blitz, and played the blitz. We won the blitz, and queued for another.
At this point we haven’t tried any other tests, but two of my healers are not capable of queueing blitz as a duo with another DPS.