I'm not sure what to tell you about cost, as we are gluten and dairy free due to celiac disease, so we can only purchase certain brands, which makes my grocery bill higher than it otherwise would be- that's a 'perk' of having a food allergy. And another good portion of your budget will depend on what you do about breakfast and lunch, and how many and what kind of snacks you buy. And if you purchase any convenience items instead of making things from scratch.
I can tell you that even with the gluten and dairy free restrictions, we spend about $500 a month for all meals for all four of us. That is an average- some months we spend more, some less, due to things like buying meat in bulk. That includes snacks, eating out (my husband only), everything. My children are also on a gluten and dairy free diet, but my husband is not. Also, what area of the country and whether or not you're purchasing organic has a major influence on budget. I buy organic staples because I'm part of a UNFI buying club, but my access to organic fruits and veggies is hit or miss due to my rural location.
Thanks so much for your replies I think I am slowly bringing him around, but it's a loooong drawn out process and I just want to turn our life up the right way already