Full backups don't truncate the log and hence don't break the log chain. In your example, it's possible to take the previous day's full backup and restore all the...
I'm not 100% certain, but my first pass at this would be querying against the definition field in the sys.all_sql_modules view in the DB in question. Something like:
Are you saying you are currently backing up the data file, then taking a transaction log backup immediately thereafter? If so, I think you'd be better served by reversing the...