My mum used to do mine when I worked full time...having given up work to look after our children 5 years ago....she STILL does it! Bless her! To be honest, if she didnt, I would farm it out. I loathe and detest ironing, but I quite enjoy all the other household chores. DH doesnt get time to do it (fair enough, I wouldnt expect him to as he is out at work all day, and Im just at home with my feet up watching Trisha...yeah right!). I have only seen my DH brandishing an iron once since we met, and it took him 15 minutes to iron one shirt!
I would trade..if he really CANT iron (a common fault in the male population!) then make a deal that he must take over some other less desirable tasks. Cleaning the toilet is a good one. Putting the grocery shopping away is something else I hate personally as well! If you dont give in, I bet he will still take it to his mum to do...mine would!