Aliens, broken English and changing POVs

Here's an interesting question:

My male protag in my WIP is human and speaks English, but my female protag is an alien and is still learning the language, thus her English is awkward, broken and she does not always understand everything he says.

So my question is, when I change from his POV to hers, should I have her hear him speak in same broken manner of which he hears her, to be consistent with the fact that she does not recognize everything he says?

Or should I have him speak normally, and just take it for granted that the reader will already know that she doesn't understand everything?

RG570 said:

I think it would be better to write what the character heard normally and then just conveyed the lack of understanding through her thoughts or dialogue. Otherwise it might get annoying.

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That's the way I was leaning, I can see it getting annoying REALLY fast if I have him butchering his words too, as it is I'm wondering how to handle it when she speaks without going overboard.

I'm also finding it tough to enter her POV without making her thinking too much like she was raised speaking English, I've caught myself having her use human measurements for time, etc. What she thinks is critical because she's half the story, and there's a limit to how simplistic a manner I can portray her thinking without hurting her character's developement.