blobService.doesBlobExist(containerName, blobName, (callbackResult: ErrorOrResult<BlobService.BlobResult>) => {
        //Want callbackResult.response here
});

doesBlobExist(container: string, blob: string, callback: ErrorOrResult<BlobService.BlobResult>): void;

interface ErrorOrResult<TResult> {
    (error: Error, result: TResult, response: ServiceResponse): void
}

blobService.doesBlobExist(containerName, blobName, (error, result, response) => {
        //i.e. specify the 3 items directly in the interface
});