I'm also one of those who is also actually saving money by eating this way. We did a poll about this a while back, and about 25% are spending less. It's because we're not eating out, descending upon the vending machines at work, going for 7-11 raids at midnight, and also just our bodies require less food volume-wise now.
Anyway, is the money his legitimate concern ... or is that just his excuse? Lots of partners are so resistant and will try to sabotage when the other begins to change and improve their life. (Been there, done that.) If so, once you can prove you are spending the same or even less, he'll just come up with another excuse at that point and will whine you to death.
"Let food be thy medicine and medicine be thy food." -- Hippocrates