I know exactly how you feel, but tbh it wouldn't be any better if he did answer the phone in front of you, especially if his ex still has feelings for him, because you'll hear the easiness and familiarity of their conversations and his tone of voice and immediately feel shit about that too! I speak from experience.
My DP's ex has no boundaries, phones him at all hours about stupid things that could easily wait until they see each other next (most days
) or could be put in a text so as not to be intrusive, but no, she'll call him and loudly greet him "Hey babe!" and he'll laugh and be all friendly to her and it just drives me up the wall!
She phoned him at midnight on NYE one year, on Valentine's day one evening while we were in bed etc and he always answers - just in case its about the DCs, which it never is. The NYE one she didn't even ask to speak to the kids, just wanted to wish him a happy new year, and Valentines was to tell him her sister was pregnant 
To be fair, even when they'd argue in the early days it made me uncomfortable. He thought it proved to me that they were incompatible, but as I said to him "the opposite of love isn't hate, its indifference, so while you think I want to see that you hate her, I don't. Your anger at her is a sign that you still feel hurt over what she did".
So these days I ask that he takes calls from her elsewhere, (and he also takes his DCs Facetime calls elsewhere now, as she always butts in on them too!) then I don't have to hear her stupid loud voice, or him giggling and simpering when she says something funny, or that the call is completely pointless and could have waited!
Honestly, be thankful that he's sparing you that shit. I know it must be hard to get over what your ex did to you, so make sure he understands that this is the reason you feel uncomfortable about it. Any amount of counselling won't erase those feelings, but it might help you to feel more relaxed about this relationship and that nobody would have been judging you for not knowing what an utter bastard your ex was. Anyone who knew and didn't tell you should be ashamed of themselves, not judging you. 