Wow, thanks for all the replies! I will definitely be using some of these techniques.
I did want to say that he is definitely not doing it to make me look stupid or to act like he's smarter than I am -- In fact, it's quite the opposite; he thinks I'm so intelligent that I should be able to figure it out even if I don't speak the language! In some cases that's true, when he speaks in Italian I can usually get the gist because I've studied Latin, and I'm beginning to catch some of the household Japanese he uses (it's his family language, and the one his father speaks most of the time so this one is more an issue of fitting into the family), but when it's Polish I'm still at a complete loss!