Since we work 12 hour days you only work 15 days a month.
Anyone who works 12 hour days deserves some time off. Don't beat yourself up over it. It was more to it than just the fact of you having free time. She is using that as an excuse.
There are many couples who deal with the same thing. I have a friend who works on the fire department and he works a 24 hour shift and off 3 days then back on. His wife said she misses him when he is gone but she knows it pays the bills.