I have added a C/C++ dylib library, with C Public API headers to Swift Project.

Assume that the library is, libModule.dylib.

1. Create a Directory with "Module"

   mkdir Module; cd Module
   

2. Create a file module.map inside Module directory

   Touch module.map
   

3. create a directory, this will be the header files directory, any name will serve.

   mkdir Headers
   

4. copy all headers into Headers directory

   cp -R path/Headers Headers/
   

5. open module.map & copy below contents to it, Swift team suggest, adding prefix C in front of library name, in case if its a C library.

   module CModule {
     umbrella "Headers"  // for multiple files
     header "filename.h" // for single header file, in this case even the Header directory is not needed.
     export *
   }
   

6. Go to Build Settings -> Swift Compiler - Search Paths

7. Add complete Module directory path to "Import Paths" key.
8. Go to Build Phases, Add New Copy Files Phase.
9. Drag libModule.dylib to the Copy Files phase. Select Destination to "Frameworks".
10. If required add the libModule.dylib to Link Binary With Libraries section of Build Phases.

If step 9 is missed, we get famous @rpath/ Image not found crash.

Now Import module in swift as below:

    import CModule // name given inside module.map

For system library, most steps don't require.. just create directory & module map file with correct header path and do 6, 7. Its seems step 10 not even required as its a system library.

    module CommonCrypto [system] {
      header "/Applications/Xcode.app/Contents/Developer/Platforms/iPhoneOS.platform/Developer/SDKs/iPhoneOS.sdk/usr/include/CommonCrypto/CommonCrypto.h"
      export *
    }

You can import system modules as described in this answer: Importing CommonCrypto in a Swift framework

TLDR

1. Add a Folder named ZLib to your framework directory
2. Add a module.map file with the following contents

module ZLib [system] { header "/Applications/Xcode-beta.app/Contents/Developer/Platforms/MacOSX.platform/Developer/SDKs/MacOSX10.11.sdk/usr/include/zlib.h" export * }

You might have to change the path to your zlib header. The example works for XCode 7 Beta and El Capitan.

3. Add the currently generated module.map file to your build settings
4. Import ZLib in your swift file and you will be ready to go