Can it be done? Yes, but is it fun? No. Is it healthy? That's sort of a major toss up on what defines healthy. First off to live on $25/week for 2 people you really need to take vitamins. We lived like this when we first meet in 2000 because we were pretty broke.
Our income just barely covered all our bills and I had student loans about $10k that I wanted to pay off in 1 year and I did. DH made $18k gross, I made $30k gross, and our rent at the time was $1100/month for 1 bd. Hey Southern CA was and still is expensive. After taxes, looking at our old paystubs DH cleared I believe $500/bimonthly and I cleared $600/bimonthly.
We also had a car loan of $150/month, high car insurance because we were independent 20 and 22 year olds with full covereage = $300/month and no other way to get to school/work. If you live in So CA, you'll understand when I say there is no public transit. So after paying all our bills, I used to budget $25/week for the two of us.
For one thing our menu rarely changed and we ate a lot of the same food. We ate a ton of pasta, tomato sauce, and ground beef. All of it was bought at costco. For variation when Chicken breast was $1.69/lb we bought that. This was our staple meal. To add vegetables we would buy either canned or frozen veggies and throw it in. We ate this about 3-4x week for lunch/dinner. Another cheap meal was rice, chinese veggies, and pork pieces. We would stir fry the pork in black bean sauce, soy sauce + sugar. We didn't eat anything else, in case we didn't make enough dinner for leftovers, our lunches were packaged noodles.
To me coupon shopping did not help because we didn't buy any prepackaged foods (too expensive). We bought tomato sauce (prego), ground beef, chicken, and pasta. There also weren't coupons for chinese veggies, rice, etc. This was the most economical shopping.
We planned our menus, shopped solely from a list, and stuck to $25/week cash. If it went a penny over we returned it. During this time we also had a lot of free food from school, friends were generous and invited us over, and when our parents visited they would graciously fill our freezer with meat.
I don't reccomend eating this way long term. I don't think it provides enough nutrients and vitamins for the daily requirements. Personally we would have cut cable if we had it, didn't have cell phones, only a home phone, shared internet with neighbors. So our only flexibility in the budget was food. As our income increased it was the first area we immediately increased. Also we probably could have spent more if we weren't trying to pay off a school loan and save a cash EF. Turns out our savings allowed us to buy a house 2 years later.
Now I guess we spend $150/month per person on groceries. We eat very luxuriously and I admit it. I buy steak, seafood, lobster, chicken, cheese, fresh veggies and fruits, pretty much anything DH desires. I still don't buy much prepackaged foods, but I do buy expensive staples. How do I justify it? Well DH says he'd rather eat good food and not watch cable than eat crap food and watch tv.