Such events have often been held in synagogues and with RC Priests at the head of the invitation list.
A Muslim is different.
That is because the Islamic scriptures teach explicitly against Jesus Christ, and because those scriptures also teach subjugation of Christians and Jews (or their murder).
I have no problem with any legitimate, decent priest, rabbi, or minister of the Bible sharing a prayer in any RC Church, Protestant Church, or Synagogue. It happens all the time and it works out just fine, too.
Acknowledging differences, we are still all praying to the same God.
Moslems do not appear to pray to the same God as do Christians or Jews. I realize that the RC Church and other Biblical faith groups have tried to reach out to Moslems.
This can be accomplished sometimes in non-Islamic countries, and so long as we stick to secular cooperation.
However, yes to answer your question I would not attend a shared service with a Moslem, as I have read their Koran and studied many of their statements and am convinced that they pray to someone very, very different indeed than the One True God of the Bible.
Very different.
(By their fruits, ye shall know them...)
But Vatican II states that Muslims worship the same God!
This is not merely semantics, either. The distinction between Jews and Christians is absolutely, irreconcilably at the very root of what defines Christianity.
I probably have no religious objection to this sort of ceremony at all, but it ought to be held in a public park or a VFW hall.