I have been saying this on MDC for the last year. I used to be able to spend $600 a month. Maybe $800. But now it's up to $1200 for 4 of us. That's not including dog food, but it does include diapers, paper towels, and cleaning stuff.
Oh and I do shop at Jewel (used to be Albertson's, now owned by SuperValu).
The only way for me to control our costs for food is to buy in bulk, stockpile and plan a heavily organized meal calendar. I also make 95% of our meals from scratch. the 5% is eating out (once a month if that) doing a happy meal treat here and there or snack type stuff. IRL, I know talking to other couples and parents we have the cheapest cost of living for meals than anyone. We used to be able to feed us for under $400 a month. Now its $500 on a good month and more like $550. That includes already fixed in costs even though its paid for- like our side of beef we bought at the beginning of the year. But it comes out to about $85 a month.