When my husband was out of work before getting SSDI we lived without natural gas. We had a microwave, a crock pot, grills, electric griddles, etc...it is very do-able. I also bought an electric dryer when I got a new one several years ago. We do have an electric water heater, that makes the difference. If you have a gas water heater you can't do without gas. Your kids could be taken away if you get reported for not having hot water.
You are going to have to sell things, have a garage sale, let cars or other extra's go, sell off some jewelry, if you have any other collectibles like guns or comic books. You things could save your family this hardship.
There is also the need for an income. I understand if your husband needs to keep the unemployment coming in as a stable sort of income but you can work. You can work at WalMart or some other place just to get some extra money coming in. You need to look down the street. Keep looking for the better paying jobs but you need to get a job and get that extra income coming in. He can watch the kids, free child care.
It won't be for long hopefully. I work 3 part time jobs to help my family. I work for the owners of the dance studio that my kids go to, I receive no money, it is trade out for the kids classes. If there is extra left over I have to take it out in trade in their clothing store. I iron for people, I ran an add in the local newspaper for a very short time and got several customers. I claim the income on our taxes every year. It gives us more earned income credit since my husbands income is non-earned income. I also clean houses, for my FIL I get a gasoline card to fill my car a couple of times a month. I have also sewn clothes, did laundry for others, helped them garden, ran errands for the elderly, etc...there is money out there but you have to be in the mind frame to go find it and make it.
I know haw hard this is for you. My husband made over $70,000 a year 20 year ago and got laid off one day. No warning. We were paying over $700 a month for car payments, over $1100 every 6 months for full coverage insurance, about $500 a month for wonderful health insurance through his company, lived in a nice home, had lots of fun eating out and spending time traveling. It was wonderful. $70,000 went a LOT further back then. We were working on being totally debt free, had savings, tithed fully, had a retirement fund, life insurance, everything we wanted.
Suddenly our cars were being repossessed, our house was 3 months behind (we ended up walking away with nothing due to repossession), credit companies were calling every day, we couldn't eat out, and my daughter had to leave private school. It was an awakening for me. He got another job pretty quickly and he was there about a year and they downsized him out of a job. It was not as shocking to me, even if it was the Monday before Christmas. We had changed a lot of our living habits and didn't live as extravagantly. We didn't get unemployment at this job ending.
You are going to have to look at your life, your possessions, your ideals...and decide what is more important. Having that unemployment is a good thing. It needs to be protected. You need to get an outside job. My husband could loose his Medicare and his other benefits if he could work. I am the one that has to go find the extra income.
It falls on you to find that short term fast income. You should keep looking for the higher income jobs but right now you need to keep your family first. Calling all the places everyone is telling you about is a short term fix. They may be able to help you once every 6 months or even once every year. Every one of these agencies is going to look at your monthly bills, how much your house is costing you, car payments, etc...if those things are what they are helping you pay.
Other things that are cash. Cash in some life insurance, sell off your retirement funds, it stinks but it is money to keep your family afloat. If someone has a serious health issue then there is health insurance through your state to help. Children get health care cards pretty easily if the income is low enough. You do need to go to a local state agency to apply for assistance anyway. You may not qualify but what is lost? Nothing.
