First, let go of the idea of what you think life "should" be like. Most people I know, myself included, have gone through extended periods of time in which meals are mostly instant noodles or mac and cheese (made with powdered, not fresh milk.) "Variety" meant having the chicken flavor for lunch and the beef flavor for dinner. Is it ideal? No. Is it normal? Yes. Will your family be malnourished and unhappy if you don't have a picture perfect meal every day? No, unless it goes on for many years at a stretch AND you make a big deal about how "poor" you are.
I grew up in a time and place where having friends over for dinner was common, and might happen several nights a week. In our household, though, we had to check with my mom well in advance, because we could only have friends on spaghetti nights. When we had anything else, there was just enough for us. When we had meat, we would have only 1 burger, pork chop, hot dog or whatever else per family member, so we couldn't have friends over on those nights. The only leftovers we ever had were boiled potato quarters - I thought it was so odd when my friends complained about leftover nights, because we never had that much food. Yet I never, EVER worried about going hungry, because I knew my mom would have something on the table every night.
You may have to re-learn how to cook. Hamburger Helper and a can of fruit cocktail is a complete meal. Sandwiches, hot dogs, pork & beans and corn bread may not be anyone's idea of the perfect meals, but no one will starve eating them! I have some great casserole recipes that I originally used because they were cheap, but my family loves them, so we keep eating them even though we can afford something pricier.
Google recipes from the Great Depression - I have a great cake recipe that uses no eggs, butter or milk.
Are you signed up for Freecycle.org? Post a notice asking if anyone has extra produce from their garden.
Even in an apartment, you can plant pots of tomatoes, carrots, onions etc. In a yard, you can plant more. Even if you can't grow any this year, make sure you get seeds (and pots, if needed) for next year.
Many food banks will not ask about your income. Call around and find out what's available near you. Our community has Kids Cafe serving places (parks, schools) where anyone under 18 can get a free dinner, no questions asked. It might not be your idea of a great dinner - it's likely to be pasta or sandwiches - but it's food.
On the flip side, it's SO aggravating to food bank workers when people say, "I'm so desperate, we'll take anything" over the phone, then show up at the food bank and wrinkle their noses in disgust and say, "I only use name brands," or, "I wanted fresh food" (most food banks only have access to cans and boxes). I've seen it happen, and it's always made me want to say, "You can't be very desperate if you won't accept this. Please leave it for someone who really needs it."
Hang in there. People who've lived through hard times are more resouceful, compassionate, capable and helpful than those who haven't. Learning how to "make do" is a good life lesson. I know it feels like you're letting your kids down, but what you're really doing is giving them skills they'll need as adults.