It would be a criminal act for use to help you to hack his account.
Instead, you should talk to your husband. Perhaps the two of you need to engage in some counseling.
One has to wonder why he would see a need to seek to fulfill his needs from other places than home.
If you want your marriage to succeed, then both of you need to realize that love is a decision not an emotion. The giddy feelings go away. Being "in love" is not an emotional state. It is something you choose to do each and every day. It is up to you to care for your husband, more than yourself, each and every day without regard to how you "feel" that day. Make him feel comfortable, secure in your relationship, wanted and cared for and you should be able to teach him to do the same for you. If you are feeling insecure, tell him so and ask him to help you to become secure as a person and as a friend and spouse.
If you wait for him to make you feel loved before you love him, then the two of you might as well give up now because he is doing the same thing and things will never get better.