Create contextually filtered view of shared fields across multiple content types
I haven't tried anything exactly like this buts it sounds like it is very possible if you mess with your AND, OR settings. Since they share the same field and that is what you are filtering on there should be no issue with that being your contextual filter.

Look at your regular filters under 'Filter Criteria'. Filter on the content type in an OR group using 'And/Or, Rearrange' (the arrow next to 'Add'). And it should work.