Chase isn't the only bank that tack's on a service charge for paying by phone. I quit doing that years ago because of the additional fee's.
Your husband is going to have to suck it up and get with the times, learn to live without CC's or risk the always fun, "you're check did not get processed in time so here's a late fee."
I've been paying bills online for several years now and will also utilized any autopay features (minimum payment in my case) so that I don't forget to make a payment or, mess up and schedule the payment for the next month rather than the current month (did that once with BOA). I don't use the automatic payment option to pay the bill in full in the event there's some sort of emergancy and I forget to change it. I'd hate to have to much money taken out of the account after I'd paid to have something unexpectedly like a new water heater, repair to furnace or ac or any other little emergancy that can befall a person without much warning.