If I'm not wrong, ofcourse you can study full-time/ part time while on an H1-B or a H-4 visa. Unlike a F-1, the benefit of an H1-B is you do not have to maintain a minimum course load (usually 3 courses per semester) to stay full-time and hence in legal status. With an H visa, you can study part time at your own pace.
If you are studying for Masters level classes (which are mostly in the evening), you should be able to manage your day-time job and evening school, like so many others have been doing. Good luck.
Jawad