"error: underlying Objective-C module <module> not found"

Apple does not promote distribution of iOS frameworks as of Xcode 6 (referring to this SO post):

Xcode 6 does not support building distributable Swift frameworks at this time and that Apple likely won't build this functionality into Xcode until its advantageous for them to do so.

However, it is not impossible to build one:

• Go to the Product menu.
• Click on Build For.
• Select Testing.

And as always, trashing Xcode's DerivedData folder (rm -rf ~/Library/Developer/Xcode/DerivedData) usually solves any trivial problems that may arise.

I was able to fix this issue. If you are importing a module that links any Objective-C frameworks, you need to import those Objective-C frameworks in your module too. That shouldn't add to your bundle size if you are not using a static library.

I imported all of the frameworks needed for Parse into one module "Module A". In order to import "Module A" into "Module B", I had to add all of the required Parse frameworks and "Module A" to my Linked Libraries for "Module B".