Not only can air scenting and trailing dogs be on the same team, they can be utilized together on a search mission.  Utilization of these two disciplines together provides a search manager with many options.  

I was sitting in a classroom in Maine in April. It was the first time I had been to Maine and met the good folks at MESARD. The instructor handed out topographical maps and different search scenarios.  We, the students, had to come up with our search strategy based on the scenario. We were allowed to ask questions to clarify the written information.  In one particular scenario, there was a point last seen, consisting of two elderly people missing from their home. They were known to go on walks around the neighborhood. I worked very diligently deciding where I was going to deploy trailing dogs and then air scenting dogs based on the clues the trailing dogs came up with. I sat very smugly in the back of the room, sure that I had completed the task correctly, and had picked the most efficient manner in which to conduct this search. The instructor began to diagram what actually took place on this search.  That is when I realized that not only are there strategic differences between search dog deployment, there are also geographical and political differences. The instructor had divided up the areas of probability nicely and deployed generic air scent dogs. When I asked about trailing dogs in combination with scent discriminating air scent dogs, there were valid political reasons as to why this team used only air scenting dogs. Even though I might have done it differently, their search was a success and resulted in the rescue of both victims. I had not even given it a thought as to what I would have done if I didn't have trailing teams because in the scenario, there was still trail scent that could have been followed.

If I am placed in the position of K9 Command, (which needs to become an official position in the incident command system, which then reports to operations/IC) I will plan a strategy that uses both trailing and air scenting dogs. Because where I am from, we have both readily available. 

Both disciplines trailing and air scenting, if separated rather than trained together, should have performance criteria that is testable to validate the training. If the dog does both, then the performance criteria is adjusted to test the dog's ability in both functions.