Can I use my enterprise developer account to sign Passbooks that will be used externally? Can I use my enterprise developer account to sign Passbooks that will be used to download tickets from a public facing website?

The reason I ask this is because in the enterprise developer program it states that I cannot have apps in the normal app store but only sign apps that would be distributed internally.
Yes - if the enterprise entity is the one distributing the pass to end users, then you should be fine using that certificate to sign Passbook items. Any Apple generated code signing certificate should be sufficient to fulfill the requirements. If you are concerned after reading this, a quick call to developer support might help alleviate any concerns you have.

Apple documents this at https://developer.apple.com/passbook/Getting_Started_with_Passbook.pdf and the version 1.1 of this document states:



Use of Apple-issued Certificates

All passes need to be signed with an Apple-issued certificate to be recognized by Passbook. Passes should only be signed by the entity that will be distributing the pass under its own name, trademark, or brand, and that entity’s information should match the information on the back of the pass.