If you have access to his computer, a keylogger may be an effective solution. This would record any keystrokes made, and it is usually (depending on the user and actions taken) fairly simple to tell which keystrokes (in this case, username and password) go to which site.
He has his own laptop and I know that he checks his history and can tell if something is changed on it.
In most cases, you would need to get on the internet to download a keylogger. I have no clue of your husband's abilities when coming to computer skills, but if looking at history is all that he would notice different, then you might try some or all of the following (my example is with IE, but this should be similar for most browsers):
*) History>Show in Sidebar(if not already there)Then proceed to right-clicking and deleting. This should get rid of select History events.
2) This may differ between browsers, but for IE6 I believe you go to Tools>Internet Options...>Then under the Temporary Internet Files Sub-section, you may want to delete cookies and files (this may depend on your husband's ability to notice if cookies/files are missing, or if there are cookies/files that weren't there before).
There are many ways to find a username/password, and this is just one of them. If you find or hear of another way, you might find that way easier or better - just know that there are many solutions out there.