You should also mention to your boss probably the biggest benefit you get from InnoDB for large tables with both read/write load - You get row-level locking rather than table-level locking. This can be a great performance benefit for the application in cases where you see a lot of waits for table locks to be released.
Of course the best way to convince your boss is to prove it. Make copies of your large table and place on a testing database. Make one version of data in MyISAM and one in InnoDB. Then run load testing against it with a load mix that approximates your current DB read/write activity. Find out for yourself if it is better.
Just updated for your comment that you are on 5.5. With 5.5 it is a no brainer to use InnoDB. MyISAM engine basically has seen no improvement over the last several years and development effort has been around InnoDB. InnoDB is THE MySQL engine of choice going forward.