It depends on whether you want to convey a mental state or an activity.
This kind of question comes up frequently for me. I am a native English speaker, but my wife is from Germany, and I sometimes get questions like this from our German friends. (For those who do not know, German has no present progressive tense, so context and additional language must be used to convey the concept).
I don't know of a hard-and-fast rule, but I have noticed the pattern that in English, verbs denoting mental states or emotion (wants, desires, hopes, wishes...) are more often placed in the simple present, even when one might think a present progressive form would be appropriate e.g., "I love this soup." **
So although the present progressive form is perfectly acceptable, my vote would be for "I miss my family;" the implication that it is current and ongoing is already implicit in the fact that it is a mental state. (Unless of course it were part of sentence such as "I am missing my family - I just can't get a clear shot from this window." :)
** Thus I think the previous McDonalds catch phrase, "I'm loving it," is actually quite brilliant, as it turns the simple mental ascent of good taste into an enjoyable activity by the sheer act of bucking the convention.