MS SQL Server Incremental(differential) backup interrupted due to Full backup
While you can't control if the backup happens, could you ask the third party to change how the backup is taken? Using the COPY_ONLY option stops backups from interrupting other backup sequences, so if they add that to their process it will stop interfering with your's. See https://msdn.microsoft.com/en-gb/library/ms191495(v=sql.120).aspx for more info.

That is the only option that doesn't require an extra copy of the database. Other than that you could maintain a replica and have the 3rd party take their backups from there (or take your backups from there).