If your husband is concerned about the small amount your bill will go up by using a heat lamp, you probably can't afford chickens, then. Seriously. If he's gonna get all twisty in the knickers about the cost of running a heat lamp, chickenkeeping may not be for your situation. That's only a miniscule expense in the venture of chickenkeeping.
I hope you can work it out.
And to answer your question, yes, it must be on 24/7 in order to maintain the temperature to keep the chicks alive. Turn it off, and you'll probably have at least several dead chicks in a few short hours, and the ones that aren't dead will have health problems and will die before long.
Think of it as putting a baby out in the cold without a blanket, even for a few minutes. It's the same thing when you turn off your heat lamp in the brooder. Would you do that to a baby? No. Doing it to your chicks would be the same thing, tho.