Are you done having children? If so he can always get a vasectomy and he wont have to worry about getting you pregnant.
There are contraceptive methods (IUD is most foolproof) that will allow your husband to not use a condom IF the regimen is followed specifically as directed. Talk to your doctor about what might be best for you given wherever you are in life.
Unfortunately, women can ovulate on an irregular schedule. If your cycles are absolutely like clockwork, and you can predict to the day when you will have your next period, then you can assume there is safety about the last four days before your period, and the first couple of days during your period. Sorry if that makes your husband grumpy. If you two are done having kids, why not a vasectomy? Then he wouldn't have to wear a condom. If you are thinking of having kids later and just don't want them now, why not look into the IUD?