HELP!! Why is my stove turning my lights and furnace back on when they go out?
You have a leg down in your utility service, so call your utility and get them to fix it

The standard North American residential utility service is a 240V split phase service with 2 "hot" legs at 120VAC and opposing in phase as well as a center "0" point i.e. the neutral.  What happens if a leg has failed or is failing in the service is that all the things on that leg will stop working until you turn on a 240V appliance connected across the legs (such as your stove), which connects them to the working hot leg through the stove.

As you have already done, the correct move is to call your utility and tell them that you have a partial power outage, or if you feel technical, that you've lost a leg of your service.  They'll come out and investigate, generally at no charge to you, as the problem's likely theirs to fix anyway, such as a burnt lug in the meter base or a problem up on the poles even.