Before the Second Vatican Council, the Church prohibited public prayers with non-Catholics. This referred specifically to public, not private, prayers, in order to avoid confusion and relativism between the different confessions and the uniqueness of the Catholic Church. Therefore, it was forbidden. Unfortunately, after the Council, the Church now allows public prayers with non-Catholics. This is not correct, because it can be a tool to undermine the uniqueness of the truth of the Catholic Church, opening the door to doctrinal relativism.
However, I think it is acceptable to pray privately with a non-Catholic Christian for a specific purpose, as long as it is done privately and not publicly. In a family setting, for example, people can pray common prayers like the Our Father or Psalms. This is acceptable, even in the case of a mixed marriage, but it should not be done publicly.
Dear visitors of Gloria Dei and all who have already written or who will write a personal message to me. I am grateful for your attention, your kindness, for your spiritual support and especially for your sacrifices and prayers for me. God may reward you!