Are interdisciplinary STEM PhDs qualified to become professors? Are interdisciplinary STEM PhDs qualified to become professors? Or are they viewed more as “in-betweeners” and better suited for industry work. For example, someone who has a broad (but not deep) math background and only relevant (but neither deep nor broad) domain knowledge in, say, biology or physics, to write their papers?  In other words, such a PhD candidate will be trained neither as a traditional mathematician nor as a biologist or physicist, etc.  

Then what typically happens after their PhD?  Do they not have deep enough knowledge to join academia as professors in any department?
Yes, interdisciplinary Ph.D.'s are qualified to end up in academia.  In fact, I think hiring interdisciplinary faculty is a quite a popular idea with university administrations, and so my feeling is that there has been a bit of a burst of interdisciplinary positions created.  If you do really excellent interdisciplinary research, I think you should have a very good chance of getting an academic job.   

I think you do correctly note some disadvantages that come along with it: hiring and tenure decisions tend to be made within departments, and interdisciplinary work can sometimes look not especially deep from the perspective of either of the disciplines, or simply be difficult to see the importance of if you don't see both perspectives.  But if people really do come to see the connection, then it will be highly valued.