Yes, there are ways to hack your husband's phone and be alerted every time he receives a message. Even more, you will be able to work out who sent the messages to your husband, and exactly what they are saying to him.
The only hitch is that, on order to do this, you will need your husband to download a special program on his phone. It can be disguised as part of another download (such as a game you've suggested to him), and will run invisibly in the background.
The information on where to get this type of application from is illegal to distribute on the internet I believe, but there are plenty of sites divulging this info.
Even CNN is running stories on how hackers operate. Here's an example: