Indeed we have. From 1978 until 2001, the United States Conference of Catholic Bishops and the Southern Baptist Convention held a series of very candid theological conversations. The official dialogue produced two reports.
The first, “To Understand Each Other,” produced in 1989, covered a variety of topics including Sacred Scripture, salvation, spirituality, church and ministry, the roles of missionaries.
The second, “Report on Sacred Scripture” was an in-depth study on how each of our traditions approaches the Bible and how we use it in the life of our communities. The dialogue also produced several study guides on such diverse topics as the environment, poverty, racism, life issues, and one very interesting one on “Sickness, Disability and Healing.” The full text of all these statements and study guides can be found here