SQL Server backup to Azure Blob with different backup plan than local backup
As @LowlyDBA pointed out "having a separate job to upload the files to Azure BLOB" is the right approach here.  You simply can't have two separate jobs managing differential or log backups.  And you don't really want to have any BACKUP command that runs for a really long time.  

Just have a single local backup plan, and a secondary job that uses AZCopy to push some or all of the resulting backup files into Azure Blob storage.

Here's an old blog post on this topic Copying SQL Server Backups to Windows Azure Storage using AzCopy.  You can also try the new Azure File Sync  service to automatically move files to Azure.