Am guessing you're probably the jealous type or your husband has maybe been giving you reasons to doubt his commitments. whatever the case, it's all up to you. But remember, some things are better left alone or unheard off. You just might be having the wrong thoughts towards your husband's behaviors. Anyways, am not meant to give advice but answer your question. So here goes..
The best way to monitor or hack a person's device to not only listen to every call record from the device, but to have complete access to the entire phone, is by using certain types of applications, some call them spy apps. These apps can do almost about anything. Using them is like making a clone of the target device. Every single information that goes in and out of the target device will be recorded. Am talking about receiving real-time messages, Emails, call history, facebook notifications, WhatsApp, calenders, alarms, etc. The tricky part is that he won't know of the app's presence on his phone because it stays hidden. And the best part is that it can only be accessed by you over the service providers website with a user account registered to you.
The first step is to find a good app and register. After that, you need to have access to the target device so you can login to your account over the internet and download the app on the phone, then install it. Lastly, activate it and turn the visibility off. As simple as that. Basically, what the app does is to keep record of all information on your registered user account over the service providers website. You can login anytime to see new records as you please.
I've had the experience of using one in the past and I was impressed. Though I can't remember the name of the app, you can do a search over the internet for desired products.