Unfortunately, the Network Analyst solver can minimize only one cost attribute to find the best path for a route to go. However, you may take advantage of using costs that can be scaled partly due to using some other sources of factors - in your cases environmental pollution values. I can think of two options to expose your extra cost field for the solver. But again, the solver will treat them equally and you cannot specify it in a way "I want my routes to be short and it is twice as important comparing for routes to be ecologic."
Since you already have one extra (and may get more costs) exposed for each road link (aka edge), you can just add a new cost attribute in the network dataset properties which would be a combination of the two travel time (or distance, for instance) and the pollution value (the output cost value can be calculated by some formula) and then you just use this for the Route network analysis layer options
You can simply load the polylines of your streets (just a copy of the feature class with the value of pollution) as a scaled cost line barrier in your network analysis layer (if you have your data as polygins - also possible to use scaled cost polygon barriers). Then when doing routing, traversing each road link will cost more if there is a scaled cost barrier located on it (line barrier) or if a road link is located within a scaled cost barrier (polygon barrier). The Route solver will scale the cost appropriately based on the pollution value and then solve the Route finding the least cost path. It is possible to have scaled barrier from different sources and you can distinguish them well when loading just by assigning a class field when doing Load Locations.
I usually approach this task with the second option since it gives me more flexibility in scaling the cost comparing to "blending" distance/time cost with the additional custom cost(s).
