A friend of mine has been asked to do a bible reading at a wedding of a friend of his. My friend is Jewish, the wedding is Christian. They have not decided if the reading willl be from the Christian bible, i.e. one of the passages on love. Are there any issues with a Jewish person doing this? However, if it is from the Hebrew bible then that would not be a problem, correct?

These are delicate issues and they call for delicate and sensitive handling, but the question you ask seems to me to miss some important background points. When you define the wedding as Christian, it sounds like that means it's going to be a religious ceremony; from an Orthodox point of view, the question of participating in another religion's ceremonies is extraordinarily fraught, and not of the kind that can be expressed in a way that would ring true for most people today.  This is especially true since there are different varieties and theologies of Christianity, and the answers might differ depending on which of those these friends observe, as well as just how observant they are.  

 

The easiest step would be to try to sidestep the questions by participating in a religiously meaningless way; if, for example, a Christian friend were getting married in a non-church ceremony and wanted someone to bear the ring, or sing a secular song, there seems little of religious content to that or many other acts that are nonetheless emotionally meaningful and express our friendship without crossing into religious complication.  To perform an act that is identifiably religious-- reading from either the Bible or the New Testament, for examples-- I think it becomes more complicated, calling for judgments about the Jewish view of that brand of Christianity. If the reading is from the New Testament, that becomes even more of a problem, but even from the Bible, it is using Scripture to support a religion that, from Judaism's view, might be theologically problematic.

 

If your friend asked me the question, I would suggest he propose reading some other poem or reading that would be meaningful to them all.  It would avoid many difficult questions whose answers are only likely to cause tension and hurt all around.

 

Your instincts are correct.  If the Bible reading the Jew is asked to read is from the Hebrew Bible, that is fine, but if the reading is from the New Testament, the Jew should not read it as part of the wedding service.  Even if the passage is about love and is theologically neutral, many of the Christians in attendance will recognize it as part of their sacred Scripture, and thus a Jew would be participating in a Christian rite in a way that is distinctly Christian.  The same happens in the reverse direction: most non-Orthodox rabbis allow the non-Jewish parent of a Bar or Bat Mitzvah to say a prayer for the country or for peace, but not any other part of our liturgy, for that would be misrepresenting the beliefs of the person saying the prayer. 

My hunch is that the passage to which you allude is from II Corinthians. It is used at many weddings and has no specific Christological references. I would treat it as any other work of poetry. Remember, actors read many lines that do not reflect their personal philosophy.