Friendly Endeavor With an Athiest

I have a friend who is an athiest (not an agnostic). He is familiar with church, Bible and arguments for the existence of God. He also describes what could be a conversion experience or at least a profession of faith in the past. We talk daily and work together on some business projects. We are similar in age, intellectual interests, aptitude and we share many moral and political values. In a safe and non-agressive manner we both freely discuss our faith (yes, I'm counting his as a faith), neither of us fearful of asking or being asked the tough questions.

In an effort to 'reach across the table' and educate ourselves as to how the other reasons for their hope, I am considering a proposition: We both read two books, one of each others choosing and and from time to time, maybe once a week or twice a month, share perspectives, agreements, disagreements, etc.; kindof like a book club of two.

If I were to make such a proposal, I would be interested in what my colleagues at baptistboard would suggest. What book would you recommend that we read and discuss together? Maybe we should read and discuss the books simultaneously? Maybe we should read my book first and then follow with his book, or vice versa? What warnings might you offer? Maybe you think that it is inherently a bad idea?

I look forward to your responses and thoughtful participation.