So this took a while but I finally got something to run on my device. Here is my setup. I created a Swift Framework called swiftlib. I added an Objective-C class called "MyClass". Basically it looks like this:

I then modified the "umbrella header" to import my new Objective-C class. The umbrella header is the name of your swift library project. So in my case, it was "swiftlib.h". This is what is inside my umbrella header file:
//
// swiftlib.h
// swiftlib
//
#import <UIKit/UIKit.h>
#import "MyClass.h"
//! Project version number for swiftlib.
FOUNDATION_EXPORT double swiftlibVersionNumber;
//! Project version string for swiftlib.
FOUNDATION_EXPORT const unsigned char swiftlibVersionString[];
// In this header, you should import all the public headers of your framework using statements like #import <swiftlib/PublicHeader.h>
Make sure to set your header class to public or you will get a compile error. Basically whatever is included in the umbrella header is exposed to users of your swift framework so it needs to be public. Select MyClass.h and open the right details bar and select the dropdown here:

I then used this Swift framework in a single view application for testing and was able to use my Objective-C class in the AppDelegate.swift like so:
func application(application: UIApplication, didFinishLaunchingWithOptions launchOptions: [NSObject: AnyObject]?) -> Bool {
// Override point for customization after application launch.
let test = MyClass.myMethod()
print("test = " + String(test))
return true
}
This compiled and ran on my device.
For those curious, this was the implementation code for the Objective-C MyClass:
#import "MyClass.h"
#import <CommonCrypto/CommonCrypto.h>
@implementation MyClass
+ (NSString *)myMethod {
NSString *key = @"test";
NSString *data = @"mytestdata";
const char *ckey = [key cStringUsingEncoding:NSASCIIStringEncoding];
const char *cdata = [data cStringUsingEncoding:NSASCIIStringEncoding];
unsigned char chmac[CC_SHA256_DIGEST_LENGTH];
CCHmac(kCCHmacAlgSHA256, ckey, strlen(ckey), cdata, strlen(cdata), chmac);
NSData *hmac = [[NSData alloc] initWithBytes:chmac length:sizeof(chmac)];
NSString *hash = [hmac base64Encoding];
return hash;
}
@end