Another idea is for your husband to set aside certain times during the evening to check and reply to e-mails and text messages. This will permit him to address important, time-sensitive items and issues. Other than during these scheduled times, the phone should be turned off or left in another room. This will also allow you to enjoy uninterrupted time with your husband and children.
Unless your husband is a doctor on call, in which case he would likely have a beeper, I do not know of a reason for him to always have to answer his phone immediately. Today, we feel that all phone calls must be answered immediately, but this is inaccurate. Most calls and e-mails can wait.
I hope my suggestions assist you and your husband in your quest for an effective solution to your problem. Hatzlachah!