Not only can you, it was designed that way. Skip Williams said in an interview several years ago re: the changes in 2e: "Of course we thought about ascending AC. But we wanted gamers to be able to play all of their existing 1e stuff with the new edition."
Our particular group plays mostly 1e, with 2e's version of bards, thief skill progression, spell spheres and specialty schools, and many monsters. Many classes get mix/matched as well with little issue.