Radio. Id say its 6 of one and half dozen of the other.
I have some great guy friends, and i will often end their texts (and they will theirs) with xx. Doesnt mean a thing, crikey i even call them "hun".
But you having just had a baby, i can completely understand where you are coming from with the insecurity and not wanting your fella to be in any situation where another female may get overfamiliar.
Try and find a comprmise, but make sure that you talk about whats upsetting you and try and get him to understand why.
I doubt very much theres anything going on or he wouldnt be bringing her home.