Moldy burger bun

My Husband and myself sat down to have a bit to eat and wanted to make quick as we had shopping to do so we ordered the same thing to speed things up the burgers arrived and we got eating, quarter way through I put my burger down to have a sip of my coke and noticed a peppery substance on my hand, not thinking much of it at the time a wiped it away and carried on eating about 2 more bites into my burger i noticed the bun wasn't as fresh as it could be but still didn't worry to much as i just thought it may have been the way I was taking bites, my husband looked up after the FINISHED his last bite of his burger and asked me what that was on the bottom of my bun as i turned it around i Noticed a really really large piece of mold on the bottom of my burger looked like it was growing from the inside out. We immediately informed management about it (took a few pics for in case) and much to my disbelieve they had the audacity to offer me another burger i immediately said no and asked for the bill as we got to the counter we were still charged for my husbands burger (I did mention we ordered exactly the same meal) as he had finished his we didn't have a choice but to pay