I also wanted to mention that Mike Maxwell has an excellent smartapp which can combine multiple SmartThings sensors into one zone. He wrote it to solve the problem of too many false alarms from motion sensors, but it can also be used for the kind of use case you're describing, where you want two doors open to trigger an event, but not just one.
Once you use his zone manager, you now have a zone device available it smartthings which you can use with any other routines are smart lighting or core or whatever.
Again, though, it's not going to run local. It's going to run in the smartthings cloud. ( at present, all custom code runs in the cloud)
If you haven't used custom code with SmartThings before, it's pretty straightforward. Basically you copy the author's code and paste it into your own account. Here's the FAQ for that:
Then if you decide that something you'd like to try, here's the other thread for the zone manager
So zone manager solves the first part of the puzzle: how to get two sensors to be treated as one zone in SmartThings.
What You do next depends on exactly what you're trying to accomplish.
You could definitely use one of the regular door chime methods to have a voice alert play once. I'm not sure how many times it would repeat, though. Anyway, here's the information on that:
Also, just in case you haven't read about core previously, it's a very powerful community created rules engine for SmartThings. You can definitely do things like repeat and have stacked conditionals and all that. You also wouldn't necessarily need the zone manager code because Core itself can look at the two different sensors. The only issue with it is it can be quite complicated to set up.
There are two threads on core that you would need if you want to use it.
The first is a peer assistance thread. That's where you can get help setting up your rules. (Core calls and individual rule a "piston")
The second is the authors thread where you would get the Core code: